[{"publication_status":"published","acknowledgement":"KTS is grateful to Christoph Thiele for valuable discussions and helpful references. LDS is grateful to Nathanaël Berestycki for valuable discussions on Gaussian Multiplicative Chaoses. The authors are grateful to an anonymous reviewer for suggestions which improved the presentation.\r\nThe authors gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the project ‘Random Riemannian Geometry’ within the SPP 2265 ‘Random Geometric Systems.'\r\nLDS gratefully acknowledges financial support from the European Research Council (grant agreement No. 716117, awarded to J. Maas) and from the Austrian Science Fund (FWF). His research was funded by the Austrian Science Fund (FWF) project 10.55776/F65 and project 10.55776/ESP208.\r\nRH, EK, and KTS gratefully acknowledge funding by the Hausdorff Center for Mathematics (project ID 390685813), and through project B03 within the CRC 1060 (project ID 211504053). RH and KTS also gratefully acknowledges financial support from the European Research Council through the ERC AdG ‘RicciBounds’ (grant agreement 694405).\r\nOpen access funding enabled and organized by Projekt DEAL.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","publisher":"Wiley","has_accepted_license":"1","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"license":"https://creativecommons.org/licenses/by/4.0/","external_id":{"arxiv":["2302.02963"],"isi":["001366948500001"]},"citation":{"chicago":"Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>. Wiley, 2025. <a href=\"https://doi.org/10.1002/mana.202400169\">https://doi.org/10.1002/mana.202400169</a>.","ista":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2025. Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. Mathematische Nachrichten. 298(1), 244–281.","ieee":"L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous,” <i>Mathematische Nachrichten</i>, vol. 298, no. 1. Wiley, pp. 244–281, 2025.","short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten 298 (2025) 244–281.","mla":"Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:<a href=\"https://doi.org/10.1002/mana.202400169\">10.1002/mana.202400169</a>.","apa":"Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2025). Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. Wiley. <a href=\"https://doi.org/10.1002/mana.202400169\">https://doi.org/10.1002/mana.202400169</a>","ama":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. 2025;298(1):244-281. doi:<a href=\"https://doi.org/10.1002/mana.202400169\">10.1002/mana.202400169</a>"},"_id":"18632","oa_version":"Published Version","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","name":"Configuration Spaces over Non-Smooth Spaces"}],"file_date_updated":"2025-01-13T10:34:42Z","OA_place":"publisher","title":"Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous","ddc":["510"],"publication":"Mathematische Nachrichten","intvolume":"       298","type":"journal_article","arxiv":1,"scopus_import":"1","OA_type":"hybrid","article_type":"original","ec_funded":1,"abstract":[{"lang":"eng","text":"For an arbitrary dimension (Formula presented.), we study: the polyharmonic Gaussian field (Formula presented.) on the discrete torus (Formula presented.), that is the random field whose law on (Formula presented.) given by (Formula presented.) where (Formula presented.) is the Lebesgue measure and (Formula presented.) is the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG) measure associated with it, that is, the random measure on (Formula presented.) (Formula presented.) where (Formula presented.) is a regularity parameter. As (Formula presented.), we prove convergence of the fields (Formula presented.) to the polyharmonic Gaussian field (Formula presented.) on the continuous torus (Formula presented.), as well as convergence of the random measures (Formula presented.) to the LQG measure (Formula presented.) on (Formula presented.), for all (Formula presented.). "}],"quality_controlled":"1","oa":1,"date_updated":"2025-04-14T07:27:49Z","doi":"10.1002/mana.202400169","volume":298,"article_processing_charge":"Yes (via OA deal)","date_published":"2025-01-01T00:00:00Z","page":"244-281","file":[{"creator":"dernst","checksum":"1dc50d156feb777c86d779fb1c9ac875","date_created":"2025-01-13T10:34:42Z","file_size":1734511,"content_type":"application/pdf","success":1,"date_updated":"2025-01-13T10:34:42Z","access_level":"open_access","file_id":"18838","relation":"main_file","file_name":"2025_MathNachrichten_DelloSchiavo.pdf"}],"author":[{"orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"},{"first_name":"Ronan","last_name":"Herry","full_name":"Herry, Ronan"},{"full_name":"Kopfer, Eva","last_name":"Kopfer","first_name":"Eva"},{"last_name":"Sturm","full_name":"Sturm, Karl Theodor","first_name":"Karl Theodor"}],"date_created":"2024-12-08T23:01:56Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"issue":"1","month":"01","publication_identifier":{"eissn":["1522-2616"],"issn":["0025-584X"]},"year":"2025"},{"OA_type":"hybrid","type":"journal_article","scopus_import":"1","arxiv":1,"intvolume":"        61","publication":"Potential Analysis","ddc":["510"],"quality_controlled":"1","abstract":[{"text":"We study random perturbations of a Riemannian manifold (M, g) by means of so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields\r\nh• : ω \u0002→ hω will act on the manifold via the conformal transformation g \u0002→ gω := e2hω g.\r\nOur focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion, spectral bound, or spectral gap change under the influence of the noise. And if so, is\r\nit possible to quantify these dependencies in terms of key parameters of the noise? Another\r\ngoal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent interest.","lang":"eng"}],"article_type":"original","doi":"10.1007/s11118-023-10118-0","volume":61,"date_updated":"2025-09-04T11:57:14Z","oa":1,"date_published":"2024-10-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"date_created":"2024-02-04T23:00:54Z","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"},{"full_name":"Kopfer, Eva","last_name":"Kopfer","first_name":"Eva"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"file":[{"date_updated":"2025-01-09T08:13:34Z","file_id":"18789","access_level":"open_access","file_name":"2024_PotentialAnalysis_DelloSchiavo.pdf","relation":"main_file","checksum":"33c688bdf296c3d8f8bbd96c7dd26037","creator":"dernst","date_created":"2025-01-09T08:13:34Z","success":1,"file_size":1294993,"content_type":"application/pdf"}],"page":"501-553","month":"10","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"year":"2024","publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","acknowledgement":"The authors would like to thank Matthias Erbar and Ronan Herry for valuable discussions on this project. They are also grateful to Nathanaël Berestycki, and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24], and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous version of the proof of Proposition 3.10. The authors feel very much indebted to an anonymous reviewer for his/her careful reading and the many valuable suggestions that have significantly contributed to the improvement of the paper. L.D.S. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC 1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65 at Institute of Science and Technology Austria. This research was funded in whole or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen Access funding enabled and organized by Projekt DEAL.","status":"public","has_accepted_license":"1","publisher":"Springer Nature","external_id":{"arxiv":["2012.06796"],"isi":["001151118800001"]},"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"citation":{"ieee":"L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” <i>Potential Analysis</i>, vol. 61. Springer Nature, pp. 501–553, 2024.","ista":"Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis. 61, 501–553.","chicago":"Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery Tour in Random Riemannian Geometry.” <i>Potential Analysis</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s11118-023-10118-0\">https://doi.org/10.1007/s11118-023-10118-0</a>.","mla":"Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.” <i>Potential Analysis</i>, vol. 61, Springer Nature, 2024, pp. 501–53, doi:<a href=\"https://doi.org/10.1007/s11118-023-10118-0\">10.1007/s11118-023-10118-0</a>.","short":"L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis 61 (2024) 501–553.","apa":"Dello Schiavo, L., Kopfer, E., &#38; Sturm, K. T. (2024). A discovery tour in random Riemannian geometry. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-023-10118-0\">https://doi.org/10.1007/s11118-023-10118-0</a>","ama":"Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian geometry. <i>Potential Analysis</i>. 2024;61:501-553. doi:<a href=\"https://doi.org/10.1007/s11118-023-10118-0\">10.1007/s11118-023-10118-0</a>"},"project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"_id":"14934","oa_version":"Published Version","title":"A discovery tour in random Riemannian geometry","OA_place":"publisher","file_date_updated":"2025-01-09T08:13:34Z"},{"volume":29,"oa":1,"date_updated":"2025-04-14T12:59:08Z","article_processing_charge":"No","date_published":"2024-01-01T00:00:00Z","type":"journal_article","scopus_import":"1","arxiv":1,"publication":"Mathematical Communications","intvolume":"        29","corr_author":"1","abstract":[{"text":"A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of maps of bounded compression/deformation by means of the measure-algebra functor and corrobo-rates the assertion that maps of bounded deformation are a natural class of morphisms for the category of complete and separable metric measure spaces.","lang":"eng"}],"quality_controlled":"1","article_type":"original","publication_identifier":{"issn":["1331-0623"],"eissn":["1848-8013"]},"year":"2024","author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo"}],"date_created":"2024-03-31T22:01:12Z","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"page":"137-142","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2304.11348"}],"month":"01","issue":"1","status":"public","publisher":"Udruga Matematicara Osijek","external_id":{"arxiv":["2304.11348"]},"publication_status":"published","acknowledgement":"The author gratefully acknowledges funding of his current position by the Austrian Science\r\nFund (FWF), grant ESPRIT208. He is grateful to Enrico Pasqualetto for pointing out some\r\nreferences on maps of bounded compression.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","title":"A characterization of maps of bounded compression","citation":{"ista":"Dello Schiavo L. 2024. A characterization of maps of bounded compression. Mathematical Communications. 29(1), 137–142.","chicago":"Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.” <i>Mathematical Communications</i>. Udruga Matematicara Osijek, 2024.","ieee":"L. Dello Schiavo, “A characterization of maps of bounded compression,” <i>Mathematical Communications</i>, vol. 29, no. 1. Udruga Matematicara Osijek, pp. 137–142, 2024.","short":"L. Dello Schiavo, Mathematical Communications 29 (2024) 137–142.","mla":"Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.” <i>Mathematical Communications</i>, vol. 29, no. 1, Udruga Matematicara Osijek, 2024, pp. 137–42.","apa":"Dello Schiavo, L. (2024). A characterization of maps of bounded compression. <i>Mathematical Communications</i>. Udruga Matematicara Osijek.","ama":"Dello Schiavo L. A characterization of maps of bounded compression. <i>Mathematical Communications</i>. 2024;29(1):137-142."},"project":[{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"oa_version":"Preprint","_id":"15252"},{"publication_identifier":{"issn":["1050-5164"]},"year":"2024","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2024-04-14T22:01:02Z","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"},{"first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","last_name":"Portinale"},{"last_name":"Sau","full_name":"Sau, Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico"}],"page":"1789-1845","month":"04","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2112.14196","open_access":"1"}],"issue":"2","doi":"10.1214/23-AAP2007","volume":34,"date_updated":"2025-09-04T13:36:00Z","oa":1,"date_published":"2024-04-01T00:00:00Z","article_processing_charge":"No","scopus_import":"1","arxiv":1,"type":"journal_article","corr_author":"1","intvolume":"        34","publication":"Annals of Applied Probability","quality_controlled":"1","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random walks on Ω dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Ω with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously derive the hydrodynamic and hydrostatic limits for SEP/SIP on Ω, and analyze their stationary nonequilibrium fluctuations. All scaling limit results for SEP/SIP concern finite-dimensional distribution convergence only, as our duality techniques do not require to establish tightness for the fields associated to the particle systems."}],"article_type":"original","title":"Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains","citation":{"short":"L. Dello Schiavo, L. Portinale, F. Sau, Annals of Applied Probability 34 (2024) 1789–1845.","mla":"Dello Schiavo, Lorenzo, et al. “Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz Domains.” <i>Annals of Applied Probability</i>, vol. 34, no. 2, Institute of Mathematical Statistics, 2024, pp. 1789–845, doi:<a href=\"https://doi.org/10.1214/23-AAP2007\">10.1214/23-AAP2007</a>.","ista":"Dello Schiavo L, Portinale L, Sau F. 2024. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. Annals of Applied Probability. 34(2), 1789–1845.","ieee":"L. Dello Schiavo, L. Portinale, and F. Sau, “Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains,” <i>Annals of Applied Probability</i>, vol. 34, no. 2. Institute of Mathematical Statistics, pp. 1789–1845, 2024.","chicago":"Dello Schiavo, Lorenzo, Lorenzo Portinale, and Federico Sau. “Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Nonequilibrium States in Lipschitz Domains.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/23-AAP2007\">https://doi.org/10.1214/23-AAP2007</a>.","ama":"Dello Schiavo L, Portinale L, Sau F. Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. <i>Annals of Applied Probability</i>. 2024;34(2):1789-1845. doi:<a href=\"https://doi.org/10.1214/23-AAP2007\">10.1214/23-AAP2007</a>","apa":"Dello Schiavo, L., Portinale, L., &#38; Sau, F. (2024). Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-AAP2007\">https://doi.org/10.1214/23-AAP2007</a>"},"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"name":"Reaching consensus in heterogeneous random opinion dynamics","_id":"3490b268-11ca-11ed-8bc3-e0ad03f48839","grant_number":"M03211"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"grant_number":"W1245","_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Dissipation and dispersion in nonlinear partial differential equations"}],"oa_version":"Preprint","_id":"15317","status":"public","publisher":"Institute of Mathematical Statistics","external_id":{"isi":["001198623200016"],"arxiv":["2112.14196"]},"isi":1,"publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","acknowledgement":"The first author gratefully acknowledges funding by the Austrian Science Fund (FWF) grant F65, by the European Research Council (ERC, grant agreement No 716117, awarded to Prof. Dr. Jan Maas). He also gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) grant ESPRIT 208.\r\nThe second author gratefully acknowledges funding by the Hausdorff Center for Mathematics at the University of Bonn. Part of this work was completed while this author was a member of the Institute of Science and Technology Austria. He gratefully acknowledges funding of his position at that time by the Austrian Science Fund (FWF) grants F65 and W1245.\r\nThe third author gratefully acknowledges funding by the Lise Meitner fellowship, Austrian Science Fund (FWF): M3211. Part of this work was completed while funded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411."},{"article_processing_charge":"No","date_published":"2024-06-01T00:00:00Z","oa":1,"date_updated":"2026-04-07T13:00:02Z","doi":"10.1090/tran/9156","volume":377,"article_type":"original","ec_funded":1,"abstract":[{"lang":"eng","text":"This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions are given in terms of the initial data, without any reference to an equilibrium point. The main results are convergence statements for gradient flow curves and proximal point sequences to a global minimiser, together with sharp quantitative estimates on the speed of convergence. These convergence results apply in the general setting of lower semicontinuous functionals on complete metric spaces, generalising recent results for smooth functionals on Rn. While the non-smooth setting covers very general spaces, it is also useful for (non)-smooth functionals on Rn.\r\n."}],"quality_controlled":"1","publication":"Transactions of the American Mathematical Society","intvolume":"       377","type":"journal_article","arxiv":1,"scopus_import":"1","year":"2024","publication_identifier":{"issn":["0002-9947"],"eissn":["1088-6850"]},"issue":"6","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.05239","open_access":"1"}],"month":"06","page":"3779-3804","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo"},{"full_name":"Maas, Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","first_name":"Francesco","last_name":"Pedrotti","full_name":"Pedrotti, Francesco"}],"date_created":"2024-06-16T22:01:06Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"isi":1,"external_id":{"arxiv":["2304.05239"],"isi":["001203273300001"]},"publisher":"American Mathematical Society","status":"public","acknowledgement":"The authors gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 716117). This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/ESP208. This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65","day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","title":"Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces","oa_version":"Preprint","_id":"17143","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"}],"citation":{"mla":"Dello Schiavo, Lorenzo, et al. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” <i>Transactions of the American Mathematical Society</i>, vol. 377, no. 6, American Mathematical Society, 2024, pp. 3779–804, doi:<a href=\"https://doi.org/10.1090/tran/9156\">10.1090/tran/9156</a>.","short":"L. Dello Schiavo, J. Maas, F. Pedrotti, Transactions of the American Mathematical Society 377 (2024) 3779–3804.","ieee":"L. Dello Schiavo, J. Maas, and F. Pedrotti, “Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces,” <i>Transactions of the American Mathematical Society</i>, vol. 377, no. 6. American Mathematical Society, pp. 3779–3804, 2024.","ista":"Dello Schiavo L, Maas J, Pedrotti F. 2024. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 377(6), 3779–3804.","chicago":"Dello Schiavo, Lorenzo, Jan Maas, and Francesco Pedrotti. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2024. <a href=\"https://doi.org/10.1090/tran/9156\">https://doi.org/10.1090/tran/9156</a>.","ama":"Dello Schiavo L, Maas J, Pedrotti F. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. <i>Transactions of the American Mathematical Society</i>. 2024;377(6):3779-3804. doi:<a href=\"https://doi.org/10.1090/tran/9156\">10.1090/tran/9156</a>","apa":"Dello Schiavo, L., Maas, J., &#38; Pedrotti, F. (2024). Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/9156\">https://doi.org/10.1090/tran/9156</a>"},"related_material":{"record":[{"id":"17336","status":"public","relation":"dissertation_contains"}]}},{"_id":"18490","oa_version":"Published Version","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"citation":{"apa":"Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2024). Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. <i>Journal of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/jlms.70003\">https://doi.org/10.1112/jlms.70003</a>","ama":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. <i>Journal of the London Mathematical Society</i>. 2024;110(5). doi:<a href=\"https://doi.org/10.1112/jlms.70003\">10.1112/jlms.70003</a>","ieee":"L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension,” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 5. London Mathematical Society, 2024.","ista":"Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2024. Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension. Journal of the London Mathematical Society. 110(5), e70003.","chicago":"Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm. “Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” <i>Journal of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/jlms.70003\">https://doi.org/10.1112/jlms.70003</a>.","mla":"Dello Schiavo, Lorenzo, et al. “Conformally Invariant Random Fields, Liouville Quantum Gravity Measures, and Random Paneitz Operators on Riemannian Manifolds of Even Dimension.” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 5, e70003, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.70003\">10.1112/jlms.70003</a>.","short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Journal of the London Mathematical Society 110 (2024)."},"file_date_updated":"2024-11-04T08:54:26Z","OA_place":"publisher","title":"Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension","acknowledgement":"The authors are grateful to Masha Gordina for helpful references, and to Nathanaël Berestycki, Baptiste Cerclé, and Ewain Gwynne for valuable comments on the first circulated version of this paper. They also would like to thank Sebastian Andres, Peter Friz, and Yizheng Yuan for pointing out an erroneous formulation in the previous version of Theorem 5.7. Moreover, KTS would liketo express his thanks to Sebastian Andres, Matthias Erbar, Martin Huesmann, and Jan Mass for stimulating discussions on previous attempts to this project. LDS gratefully acknowledges financial support from the European Research Council (grant agreement No 716117, awarded to J. Maas), from the Austrian Science Fund (FWF) project 10.55776/ESP208, and from the Austrian Science Fund (FWF) project 10.55776/F65.RH, EK, and KTS gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the project “Random Riemannian Geometry” within the SPP 2265 “Random Geomet-ric Systems,” through the Hausdorff Center for Mathematics (project ID 390685813), and through project B03 within the CRC 1060 (project ID 211504053). RH and KTS also gratefully acknowledge financial support from the European Research Council through the ERC AdG “RicciBounds”(grant agreement 694405).Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. Open access funding enabled and organized by Projekt DEAL.","day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"external_id":{"isi":["001351918100029"]},"publisher":"London Mathematical Society","article_number":"e70003","status":"public","has_accepted_license":"1","issue":"5","month":"11","file":[{"file_id":"18497","access_level":"open_access","date_updated":"2024-11-04T08:54:26Z","file_name":"2024_JourLondonMathSoc_Schiavo.pdf","relation":"main_file","date_created":"2024-11-04T08:54:26Z","checksum":"143816823b5f43bd3748da8e3e91cef5","creator":"dernst","content_type":"application/pdf","success":1,"file_size":911476}],"author":[{"full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"last_name":"Herry","full_name":"Herry, Ronan","first_name":"Ronan"},{"first_name":"Eva","last_name":"Kopfer","full_name":"Kopfer, Eva"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"date_created":"2024-11-03T23:01:44Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"year":"2024","publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"article_type":"original","ec_funded":1,"abstract":[{"lang":"eng","text":"For large classes of even-dimensional Riemannian manifolds (Formula presented.), we construct and analyze conformally invariant random fields. These centered Gaussian fields (Formula presented.), called co-polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: (Formula presented.). They share a fundamental quasi-invariance property under conformal transformations. In terms of the co-polyharmonic Gaussian field (Formula presented.), we define the Liouville Quantum Gravity measure, a random measure on (Formula presented.), heuristically given as (Formula presented.) and rigorously obtained as almost sure weak limit of the right-hand side with (Formula presented.) replaced by suitable regular approximations (Formula presented.). In terms on the Liouville Quantum Gravity measure, we define the Liouville Brownian motion on (Formula presented.) and the random GJMS operators. Finally, we present an approach to a conformal field theory in arbitrary even dimension with an ansatz based on Branson's (Formula presented.) -curvature: we give a rigorous meaning to the Polyakov–Liouville measure (Formula presented.) and we derive the corresponding conformal anomaly. The set of admissible manifolds is conformally invariant. It includes all compact 2-dimensional Riemannian manifolds, all compact non-negatively curved Einstein manifolds of even dimension, and large classes of compact hyperbolic manifolds of even dimension. However, not every compact even-dimensional Riemannian manifold is admissible. Our results concerning the logarithmic divergence of the kernel (Formula presented.) rely on new sharp estimates for heat kernels and higher order Green kernels on arbitrary closed manifolds. "}],"quality_controlled":"1","publication":"Journal of the London Mathematical Society","ddc":["510"],"intvolume":"       110","type":"journal_article","OA_type":"hybrid","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","date_published":"2024-11-01T00:00:00Z","oa":1,"date_updated":"2025-09-08T14:29:45Z","doi":"10.1112/jlms.70003","volume":110},{"page":"957-1010","file":[{"date_updated":"2024-10-01T07:31:56Z","access_level":"open_access","file_id":"18164","relation":"main_file","file_name":"2024_JourEcolePolytechniqueMath_DelloSchiavo.pdf","creator":"dernst","checksum":"5a51da5fb5f7fcaada378d43444cced8","date_created":"2024-10-01T07:31:56Z","success":1,"file_size":1250553,"content_type":"application/pdf"}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"},{"first_name":"Ronan","last_name":"Herry","full_name":"Herry, Ronan"},{"first_name":"Kohei","full_name":"Suzuki, Kohei","last_name":"Suzuki"}],"date_created":"2024-09-29T22:01:38Z","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"month":"01","publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"year":"2024","ddc":["510"],"publication":"Journal de l'Ecole Polytechnique - Mathematiques","intvolume":"        11","corr_author":"1","arxiv":1,"scopus_import":"1","type":"journal_article","article_type":"original","abstract":[{"lang":"eng","text":"We study the geometry of Poisson point processes from the point of view of optimal transport and Ricci lower bounds. We construct a Riemannian structure on the space of point processes and the associated distance W that corresponds to the Benamou–Brenier variational formula. Our main tool is a non-local continuity equation formulated with the difference operator. The closure of the domain of the relative entropy is a complete geodesic space, when endowed with \r\nW. The geometry of this non-local infinite-dimensional space is analogous to that of spaces with positive Ricci curvature. Among others: (a) the Ornstein–Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has an entropic Ricci curvature bounded from below by 1; (c) W satisfies an HWI inequality."},{"text":"Nous étudions la géométrie des processus ponctuels de Poisson à travers le prisme du transport optimal et de la minoration de la courbure de Ricci. Nous construisons une structure\r\nriemannienne sur l’espace des processus ponctuels et la distance associée W qui concorde avec la formulation variationnelle de Benamou–Brenier. Notre analyse repose sur une équation de continuité non locale définie à l’aide de l’opérateur de différence. La fermeture du domaine de l’entropie relative, équipé de W, est un espace géodésique complet. La géométrie de cet espace non local et de dimension infinie est analogue à celle des espaces à courbure de Ricci strictement positive. Entre autres : (a) le semi-groupe d’Ornstein–Uhlenbeck est le flot du gradient de l’entropie relative ; (b) l’espace de Poisson a une courbure de Ricci entropique minorée par 1 ; (c) W satisfait une inégalité HWI.","lang":"fre"}],"quality_controlled":"1","oa":1,"date_updated":"2025-09-08T09:50:50Z","doi":"10.5802/jep.270","volume":11,"article_processing_charge":"Yes","date_published":"2024-01-01T00:00:00Z","citation":{"ama":"Dello Schiavo L, Herry R, Suzuki K. Wasserstein geometry and Ricci curvature bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. 2024;11:957-1010. doi:<a href=\"https://doi.org/10.5802/jep.270\">10.5802/jep.270</a>","apa":"Dello Schiavo, L., Herry, R., &#38; Suzuki, K. (2024). Wasserstein geometry and Ricci curvature bounds for Poisson spaces. <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique. <a href=\"https://doi.org/10.5802/jep.270\">https://doi.org/10.5802/jep.270</a>","short":"L. Dello Schiavo, R. Herry, K. Suzuki, Journal de l’Ecole Polytechnique - Mathematiques 11 (2024) 957–1010.","mla":"Dello Schiavo, Lorenzo, et al. “Wasserstein Geometry and Ricci Curvature Bounds for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 11, Ecole Polytechnique, 2024, pp. 957–1010, doi:<a href=\"https://doi.org/10.5802/jep.270\">10.5802/jep.270</a>.","chicago":"Dello Schiavo, Lorenzo, Ronan Herry, and Kohei Suzuki. “Wasserstein Geometry and Ricci Curvature Bounds for Poisson Spaces.” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>. Ecole Polytechnique, 2024. <a href=\"https://doi.org/10.5802/jep.270\">https://doi.org/10.5802/jep.270</a>.","ista":"Dello Schiavo L, Herry R, Suzuki K. 2024. Wasserstein geometry and Ricci curvature bounds for Poisson spaces. Journal de l’Ecole Polytechnique - Mathematiques. 11, 957–1010.","ieee":"L. Dello Schiavo, R. Herry, and K. Suzuki, “Wasserstein geometry and Ricci curvature bounds for Poisson spaces,” <i>Journal de l’Ecole Polytechnique - Mathematiques</i>, vol. 11. Ecole Polytechnique, pp. 957–1010, 2024."},"_id":"18158","oa_version":"Published Version","file_date_updated":"2024-10-01T07:31:56Z","title":"Wasserstein geometry and Ricci curvature bounds for Poisson spaces","publication_status":"published","day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Ecole Polytechnique","has_accepted_license":"1","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"external_id":{"isi":["001367254000003"],"arxiv":["2303.00398"]}},{"publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"year":"2023","file":[{"relation":"main_file","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","date_updated":"2023-01-20T10:45:06Z","access_level":"open_access","file_id":"12325","content_type":"application/pdf","success":1,"file_size":422612,"creator":"dernst","checksum":"1f34f3e2cb521033de6154f274ea3a4e","date_created":"2023-01-20T10:45:06Z"}],"author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","full_name":"Wirth, Melchior"}],"date_created":"2023-01-08T23:00:53Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"issue":"1","month":"01","oa":1,"date_updated":"2025-04-23T08:45:56Z","volume":23,"doi":"10.1007/s00028-022-00859-7","article_processing_charge":"Yes (via OA deal)","date_published":"2023-01-01T00:00:00Z","publication":"Journal of Evolution Equations","ddc":["510"],"intvolume":"        23","corr_author":"1","type":"journal_article","scopus_import":"1","article_type":"original","abstract":[{"lang":"eng","text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces."}],"ec_funded":1,"quality_controlled":"1","file_date_updated":"2023-01-20T10:45:06Z","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","pmid":1,"citation":{"mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>.","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>","apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>"},"_id":"12104","oa_version":"Published Version","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"publisher":"Springer Nature","article_number":"9","status":"public","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"external_id":{"pmid":["36597554"],"isi":["000906214600004"]},"publication_status":"published","acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"language":[{"iso":"eng"}],"date_created":"2023-06-18T22:00:48Z","department":[{"_id":"JaMa"}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"},{"full_name":"Lytvynov, Eugene","last_name":"Lytvynov","first_name":"Eugene"}],"file":[{"creator":"dernst","checksum":"4a543fe4b3f9e747cc52167c17bfb524","date_created":"2023-06-19T09:37:40Z","file_size":271434,"success":1,"content_type":"application/pdf","date_updated":"2023-06-19T09:37:40Z","access_level":"open_access","file_id":"13152","relation":"main_file","file_name":"2023_ElectronCommProbability_Schiavo.pdf"}],"page":"1-12","month":"05","publication_identifier":{"eissn":["1083-589X"]},"year":"2023","type":"journal_article","scopus_import":"1","intvolume":"        28","corr_author":"1","publication":"Electronic Communications in Probability","ddc":["510"],"quality_controlled":"1","abstract":[{"text":"We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.","lang":"eng"}],"article_type":"original","doi":"10.1214/23-ECP528","volume":28,"date_updated":"2025-04-14T12:59:08Z","oa":1,"date_published":"2023-05-05T00:00:00Z","article_processing_charge":"No","citation":{"apa":"Dello Schiavo, L., &#38; Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>","ama":"Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. 2023;28:1-12. doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>","ieee":"L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023.","ista":"Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12.","chicago":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>.","mla":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>.","short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12."},"project":[{"name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208"}],"_id":"13145","oa_version":"Published Version","title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","file_date_updated":"2023-06-19T09:37:40Z","publication_status":"published","day":"05","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Research supported by the Sfb 1060 The Mathematics of Emergent Effects (University of Bonn). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208.","has_accepted_license":"1","status":"public","publisher":"Institute of Mathematical Statistics","external_id":{"isi":["001042025400001"]},"isi":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"}},{"article_processing_charge":"No","date_published":"2023-09-20T00:00:00Z","doi":"10.48550/arXiv.2309.11292","oa":1,"date_updated":"2025-11-24T13:53:48Z","abstract":[{"lang":"eng","text":"We present an elementary non-recursive formula for the multivariate moments\r\nof the Dirichlet distribution on the standard simplex, in terms of the pattern\r\ninventory of the moments' exponents. We obtain analog formulas for the\r\nmultivariate moments of the Dirichlet-Ferguson and Gamma measures. We further\r\nintroduce a polychromatic analogue of Ewens sampling formula on colored integer\r\npartitions, discuss its relation with suitable extensions of Hoppe's urn model\r\nand of the Chinese restaurant process, and prove that it satisfies an adapted\r\nnotion of consistency in the sense of Kingman."}],"OA_type":"green","arxiv":1,"type":"preprint","publication":"arXiv","corr_author":"1","year":"2023","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.11292","open_access":"1"}],"month":"09","keyword":["Dirichlet distribution","Ewens sampling formula","Hoppe urn model","colored partitions"],"author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo"},{"full_name":"Quattrocchi, Filippo","last_name":"Quattrocchi","orcid":"0009-0000-9773-1931","first_name":"Filippo","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308"}],"language":[{"iso":"eng"}],"date_created":"2025-10-28T13:13:08Z","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"external_id":{"arxiv":["2309.11292"]},"status":"public","article_number":"2309.11292","acknowledgement":"This research was funded by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. F.Q. gratefully acknowledges support by the Austrian Science Fund (FWF), Project SFB F65. The authors are grateful to Professor Nathanaël Berestycki for several helpful suggestions, and to Nicola Battisti and Dr. Elizabeth Hollwey for enlightening discussions on DNA-methylation.","day":"20","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"draft","title":"Multivariate Dirichlet moments and a polychromatic Ewens sampling formula","OA_place":"repository","project":[{"grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","name":"Configuration Spaces over Non-Smooth Spaces"},{"name":"Taming Complexity in Partial Differential Systems","call_identifier":"FWF","grant_number":"F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425"}],"_id":"20572","oa_version":"Preprint","citation":{"mla":"Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments and a Polychromatic Ewens Sampling Formula.” <i>ArXiv</i>, 2309.11292, doi:<a href=\"https://doi.org/10.48550/arXiv.2309.11292\">10.48550/arXiv.2309.11292</a>.","short":"L. Dello Schiavo, F. Quattrocchi, ArXiv (n.d.).","ista":"Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv, 2309.11292.","chicago":"Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments and a Polychromatic Ewens Sampling Formula.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2309.11292\">https://doi.org/10.48550/arXiv.2309.11292</a>.","ieee":"L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a polychromatic Ewens sampling formula,” <i>arXiv</i>. .","ama":"Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2309.11292\">10.48550/arXiv.2309.11292</a>","apa":"Dello Schiavo, L., &#38; Quattrocchi, F. (n.d.). Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2309.11292\">https://doi.org/10.48550/arXiv.2309.11292</a>"}},{"intvolume":"        58","corr_author":"1","publication":"Potential Analysis","ddc":["510"],"scopus_import":"1","arxiv":1,"type":"journal_article","article_type":"original","quality_controlled":"1","ec_funded":1,"abstract":[{"text":"We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique.","lang":"eng"}],"date_updated":"2025-04-14T07:27:46Z","oa":1,"doi":"10.1007/s11118-021-09951-y","volume":58,"date_published":"2023-03-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","file":[{"date_updated":"2023-10-04T09:18:59Z","file_id":"14387","access_level":"open_access","file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf","relation":"main_file","checksum":"625526482be300ca7281c91c30d41725","creator":"dernst","date_created":"2023-10-04T09:18:59Z","file_size":806391,"content_type":"application/pdf","success":1}],"page":"573-615","date_created":"2021-10-17T22:01:17Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"}],"month":"03","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"year":"2023","publication_status":"published","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper.","publisher":"Springer Nature","has_accepted_license":"1","status":"public","isi":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2003.01366"],"isi":["000704213400001"]},"citation":{"mla":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>, vol. 58, Springer Nature, 2023, pp. 573–615, doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>.","short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.","ista":"Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.","ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” <i>Potential Analysis</i>, vol. 58. Springer Nature, pp. 573–615, 2023.","chicago":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>.","ama":"Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. 2023;58:573-615. doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>","apa":"Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>"},"oa_version":"Published Version","_id":"10145","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"file_date_updated":"2023-10-04T09:18:59Z","title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications"},{"quality_controlled":"1","ec_funded":1,"abstract":[{"text":"We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.","lang":"eng"}],"article_type":"original","scopus_import":"1","arxiv":1,"type":"journal_article","corr_author":"1","intvolume":"        50","publication":"Annals of Probability","date_published":"2022-03-01T00:00:00Z","article_processing_charge":"No","doi":"10.1214/21-AOP1541","volume":50,"date_updated":"2025-04-14T07:27:47Z","oa":1,"month":"03","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1811.11598"}],"issue":"2","date_created":"2022-05-08T22:01:44Z","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"author":[{"full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"page":"591-648","year":"2022","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Research supported by the Sonderforschungsbereich 1060 and the Hausdorff Center for Mathematics. The author gratefully acknowledges funding of his current position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr. Jan Maas).","publication_status":"published","external_id":{"arxiv":["1811.11598"],"isi":["000773518500005"]},"isi":1,"status":"public","publisher":"Institute of Mathematical Statistics","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"oa_version":"Preprint","_id":"11354","citation":{"ista":"Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.","chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>.","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” <i>Annals of Probability</i>, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","mla":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>.","apa":"Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>","ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. 2022;50(2):591-648. doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>"},"title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold"},{"volume":9,"doi":"10.1090/bproc/134","oa":1,"date_updated":"2025-04-14T07:27:48Z","article_processing_charge":"No","date_published":"2022-11-02T00:00:00Z","scopus_import":"1","type":"journal_article","publication":"Proceedings of the American Mathematical Society, Series B","ddc":["510"],"corr_author":"1","intvolume":"         9","ec_funded":1,"abstract":[{"lang":"eng","text":"Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds."}],"quality_controlled":"1","article_type":"original","publication_identifier":{"issn":["2330-1511"]},"year":"2022","author":[{"full_name":"Cremaschi, Tommaso","last_name":"Cremaschi","first_name":"Tommaso"},{"full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"department":[{"_id":"JaMa"}],"date_created":"2023-01-12T12:12:17Z","language":[{"iso":"eng"}],"page":"445-459","file":[{"file_name":"2022_ProceedingsAMS_Cremaschi.pdf","relation":"main_file","date_updated":"2023-01-26T13:02:07Z","file_id":"12404","access_level":"open_access","file_size":326471,"content_type":"application/pdf","success":1,"checksum":"cb4a79937c1f60d4c329a10ee797f0d2","creator":"dernst","date_created":"2023-01-26T13:02:07Z"}],"month":"11","issue":"43","status":"public","has_accepted_license":"1","publisher":"American Mathematical Society","tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)"},"publication_status":"published","acknowledgement":"The first author was partially supported by the National Science Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester. The second author gratefully acknowledges funding by the Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche Forschungsgemeinschaft through the SPP 2265.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"02","title":"Effective contraction of Skinning maps","file_date_updated":"2023-01-26T13:02:07Z","citation":{"apa":"Cremaschi, T., &#38; Dello Schiavo, L. (2022). Effective contraction of Skinning maps. <i>Proceedings of the American Mathematical Society, Series B</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/bproc/134\">https://doi.org/10.1090/bproc/134</a>","ama":"Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. <i>Proceedings of the American Mathematical Society, Series B</i>. 2022;9(43):445-459. doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>","ieee":"T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,” <i>Proceedings of the American Mathematical Society, Series B</i>, vol. 9, no. 43. American Mathematical Society, pp. 445–459, 2022.","ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.","chicago":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>. American Mathematical Society, 2022. <a href=\"https://doi.org/10.1090/bproc/134\">https://doi.org/10.1090/bproc/134</a>.","short":"T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459.","mla":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>."},"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"_id":"12177","oa_version":"Published Version"},{"publication_status":"published","acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","has_accepted_license":"1","publisher":"Springer Nature","external_id":{"isi":["000734150200001"],"arxiv":["2110.05137"]},"isi":1,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"citation":{"mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>.","short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>.","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” <i>Mathematische Annalen</i>, vol. 384. Springer Nature, pp. 1815–1832, 2022.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. 2022;384:1815-1832. doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>"},"project":[{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"_id":"10588","oa_version":"Published Version","title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","file_date_updated":"2022-01-03T11:08:31Z","scopus_import":"1","type":"journal_article","arxiv":1,"ddc":["510"],"publication":"Mathematische Annalen","corr_author":"1","intvolume":"       384","ec_funded":1,"abstract":[{"text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.","lang":"eng"}],"quality_controlled":"1","article_type":"original","volume":384,"doi":"10.1007/s00208-021-02331-2","oa":1,"date_updated":"2025-04-14T07:27:46Z","article_processing_charge":"Yes (via OA deal)","date_published":"2022-12-01T00:00:00Z","author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"},{"first_name":"Kohei","last_name":"Suzuki","full_name":"Suzuki, Kohei"}],"language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2022-01-02T23:01:35Z","page":"1815-1832","file":[{"checksum":"2593abbf195e38efa93b6006b1e90eb1","creator":"alisjak","date_created":"2022-01-03T11:08:31Z","content_type":"application/pdf","file_size":410090,"success":1,"date_updated":"2022-01-03T11:08:31Z","file_id":"10596","access_level":"open_access","file_name":"2021_MathAnn_DelloSchiavo.pdf","relation":"main_file"}],"month":"12","keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"year":"2022"},{"article_type":"original","quality_controlled":"1","ec_funded":1,"abstract":[{"text":"We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms.","lang":"eng"}],"intvolume":"       281","corr_author":"1","publication":"Journal of Functional Analysis","arxiv":1,"scopus_import":"1","type":"journal_article","date_published":"2021-09-15T00:00:00Z","article_processing_charge":"No","date_updated":"2025-04-14T07:27:45Z","oa":1,"volume":281,"doi":"10.1016/j.jfa.2021.109234","issue":"11","month":"09","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2008.01492","open_access":"1"}],"department":[{"_id":"JaMa"}],"date_created":"2021-10-03T22:01:21Z","language":[{"iso":"eng"}],"author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"},{"first_name":"Kohei","last_name":"Suzuki","full_name":"Suzuki, Kohei"}],"year":"2021","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"day":"15","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The authors are grateful to Professor Kazuhiro Kuwae for kindly providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They wish to express their deepest gratitude to an anonymous Reviewer, whose punctual remarks and comments greatly improved the accessibility and overall quality of the initial submission. This work was completed while L.D.S. was a member of the Institut für Angewandte Mathematik of the University of Bonn. He acknowledges funding of his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center) 1060 - project number 211504053. He also acknowledges funding of his current position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465.","publication_status":"published","isi":1,"external_id":{"isi":["000703896600005"],"arxiv":["2008.01492"]},"article_number":"109234","publisher":"Elsevier","status":"public","_id":"10070","oa_version":"Preprint","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"citation":{"short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>, vol. 281, no. 11, 109234, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>.","ista":"Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 281(11), 109234.","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” <i>Journal of Functional Analysis</i>, vol. 281, no. 11. Elsevier, 2021.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>.","ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. 2021;281(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>"},"title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces"}]