[{"publication_status":"published","quality_controlled":"1","oa":1,"arxiv":1,"publication_identifier":{"eissn":["1522-2616"],"issn":["0025-584X"]},"project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_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"}],"author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo"},{"full_name":"Herry, Ronan","last_name":"Herry","first_name":"Ronan"},{"first_name":"Eva","last_name":"Kopfer","full_name":"Kopfer, Eva"},{"first_name":"Karl Theodor","full_name":"Sturm, Karl Theodor","last_name":"Sturm"}],"file_date_updated":"2025-01-13T10:34:42Z","citation":{"short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten 298 (2025) 244–281.","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>","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.","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>","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>.","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.","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>."},"abstract":[{"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.). ","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Wiley","year":"2025","date_published":"2025-01-01T00:00:00Z","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.","file":[{"success":1,"relation":"main_file","date_created":"2025-01-13T10:34:42Z","creator":"dernst","access_level":"open_access","file_size":1734511,"content_type":"application/pdf","file_name":"2025_MathNachrichten_DelloSchiavo.pdf","checksum":"1dc50d156feb777c86d779fb1c9ac875","file_id":"18838","date_updated":"2025-01-13T10:34:42Z"}],"month":"01","title":"Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous","day":"01","publication":"Mathematische Nachrichten","OA_type":"hybrid","issue":"1","ddc":["510"],"article_type":"original","intvolume":"       298","type":"journal_article","page":"244-281","date_updated":"2025-04-14T07:27:49Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"_id":"18632","doi":"10.1002/mana.202400169","department":[{"_id":"JaMa"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","OA_place":"publisher","fulldoi":"https://doi.org/10.1002/mana.202400169","external_id":{"arxiv":["2302.02963"],"isi":["001366948500001"]},"volume":298,"date_created":"2024-12-08T23:01:56Z","isi":1,"has_accepted_license":"1","language":[{"iso":"eng"}],"oa_version":"Published Version"},{"issue":"6","day":"01","publication":"Transactions of the American Mathematical Society","intvolume":"       377","article_type":"original","type":"journal_article","year":"2024","title":"Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces","month":"06","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","date_published":"2024-06-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"researchdata_availability":"no","author":[{"last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","first_name":"Jan","last_name":"Maas","full_name":"Maas, Jan"},{"first_name":"Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","last_name":"Pedrotti","full_name":"Pedrotti, Francesco"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"17336"}]},"citation":{"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>","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>.","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.","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>.","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>","short":"L. Dello Schiavo, J. Maas, F. Pedrotti, Transactions of the American Mathematical Society 377 (2024) 3779–3804.","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."},"supplementarymaterial":"yes","publisher":"American Mathematical Society","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","publication_status":"published","publication_identifier":{"issn":["0002-9947"],"eissn":["1088-6850"]},"project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_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"}],"oa":1,"arxiv":1,"isi":1,"date_created":"2024-06-16T22:01:06Z","language":[{"iso":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.05239","open_access":"1"}],"volume":377,"fulldoi":"https://doi.org/10.1090/tran/9156","external_id":{"isi":["001203273300001"],"arxiv":["2304.05239"]},"das_tickbox":"0","department":[{"_id":"JaMa"}],"status":"public","scopus_import":"1","date_updated":"2026-10-02T12:13:16Z","page":"3779-3804","_id":"17143","doi":"10.1090/tran/9156","article_processing_charge":"No","ec_funded":1},{"type":"journal_article","article_type":"original","intvolume":"        29","publication":"Mathematical Communications","day":"01","issue":"1","date_published":"2024-01-01T00:00:00Z","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.","title":"A characterization of maps of bounded compression","month":"01","year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Udruga Matematicara Osijek","supplementarymaterial":"no","citation":{"short":"L. Dello Schiavo, Mathematical Communications 29 (2024) 137–142.","ama":"Dello Schiavo L. A characterization of maps of bounded compression. <i>Mathematical Communications</i>. 2024;29(1):137-142.","ista":"Dello Schiavo L. 2024. A characterization of maps of bounded compression. Mathematical Communications. 29(1), 137–142.","apa":"Dello Schiavo, L. (2024). A characterization of maps of bounded compression. <i>Mathematical Communications</i>. Udruga Matematicara Osijek.","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.","chicago":"Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.” <i>Mathematical Communications</i>. Udruga Matematicara Osijek, 2024.","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."},"author":[{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"}],"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"}],"researchdata_availability":"no","corr_author":"1","arxiv":1,"oa":1,"publication_identifier":{"issn":["1331-0623"],"eissn":["1848-8013"]},"project":[{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"publication_status":"published","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.11348","open_access":"1"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"date_created":"2024-03-31T22:01:12Z","das_tickbox":"0","external_id":{"arxiv":["2304.11348"]},"volume":29,"status":"public","department":[{"_id":"JaMa"}],"article_processing_charge":"No","_id":"15252","page":"137-142","date_updated":"2026-10-02T12:15:11Z","scopus_import":"1"},{"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"London Mathematical Society","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo"},{"first_name":"Ronan","last_name":"Herry","full_name":"Herry, Ronan"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"supplementarymaterial":"no","file_date_updated":"2024-11-04T08:54:26Z","citation":{"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.","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>.","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>","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.","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>","short":"L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Journal of the London Mathematical Society 110 (2024)."},"researchdata_availability":"not applicable","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. "}],"oa":1,"project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"publication_status":"published","quality_controlled":"1","intvolume":"       110","article_type":"original","type":"journal_article","day":"01","publication":"Journal of the London Mathematical Society","OA_type":"hybrid","issue":"5","ddc":["510"],"date_published":"2024-11-01T00:00:00Z","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.","file":[{"file_size":911476,"content_type":"application/pdf","date_updated":"2024-11-04T08:54:26Z","checksum":"143816823b5f43bd3748da8e3e91cef5","file_name":"2024_JourLondonMathSoc_Schiavo.pdf","file_id":"18497","success":1,"relation":"main_file","date_created":"2024-11-04T08:54:26Z","access_level":"open_access","creator":"dernst"}],"month":"11","title":"Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension","year":"2024","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","OA_place":"publisher","department":[{"_id":"JaMa"}],"article_number":"e70003","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","doi":"10.1112/jlms.70003","_id":"18490","scopus_import":"1","date_updated":"2026-10-02T12:17:50Z","language":[{"iso":"eng"}],"oa_version":"Published Version","date_created":"2024-11-03T23:01:44Z","isi":1,"has_accepted_license":"1","das_tickbox":"0","fulldoi":"https://doi.org/10.1112/jlms.70003","external_id":{"isi":["001351918100029"]},"volume":110},{"type":"journal_article","article_type":"original","intvolume":"        34","publication":"Annals of Applied Probability","day":"01","issue":"2","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.","date_published":"2024-04-01T00:00:00Z","month":"04","title":"Scaling limits of random walks, harmonic profiles, and stationary nonequilibrium states in Lipschitz domains","year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Institute of Mathematical Statistics","supplementarymaterial":"no","citation":{"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.","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>","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>.","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>.","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>"},"author":[{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"},{"full_name":"Portinale, Lorenzo","last_name":"Portinale","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Sau, Federico","last_name":"Sau","id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico"}],"abstract":[{"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.","lang":"eng"}],"researchdata_availability":"no","corr_author":"1","arxiv":1,"oa":1,"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","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"},{"grant_number":"M03211","_id":"3490b268-11ca-11ed-8bc3-e0ad03f48839","name":"Reaching consensus in heterogeneous random opinion dynamics"},{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"grant_number":"W1245","call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and dispersion in nonlinear partial differential equations"}],"publication_identifier":{"issn":["1050-5164"]},"publication_status":"published","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.14196"}],"oa_version":"Preprint","language":[{"iso":"eng"}],"date_created":"2024-04-14T22:01:02Z","isi":1,"das_tickbox":"0","external_id":{"arxiv":["2112.14196"],"isi":["001198623200016"]},"fulldoi":"https://doi.org/10.1214/23-AAP2007","volume":34,"status":"public","department":[{"_id":"JaMa"}],"ec_funded":1,"article_processing_charge":"No","doi":"10.1214/23-AAP2007","_id":"15317","page":"1789-1845","scopus_import":"1","date_updated":"2026-10-02T12:15:34Z"},{"article_number":"9","department":[{"_id":"JaMa"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","date_updated":"2025-04-23T08:45:56Z","scopus_import":"1","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","_id":"12104","doi":"10.1007/s00028-022-00859-7","date_created":"2023-01-08T23:00:53Z","has_accepted_license":"1","isi":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"external_id":{"isi":["000906214600004"],"pmid":["36597554"]},"fulldoi":"https://doi.org/10.1007/s00028-022-00859-7","volume":23,"citation":{"short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (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>","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","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>","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>.","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>.","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."},"file_date_updated":"2023-01-20T10:45:06Z","author":[{"orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo"},{"full_name":"Wirth, Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","first_name":"Melchior"}],"abstract":[{"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.","lang":"eng"}],"corr_author":"1","pmid":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","publication_status":"published","quality_controlled":"1","oa":1,"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","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"},{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}],"publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"publication":"Journal of Evolution Equations","day":"01","issue":"1","ddc":["510"],"type":"journal_article","article_type":"original","intvolume":"        23","year":"2023","date_published":"2023-01-01T00:00:00Z","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).","file":[{"success":1,"relation":"main_file","access_level":"open_access","creator":"dernst","date_created":"2023-01-20T10:45:06Z","content_type":"application/pdf","file_size":422612,"file_id":"12325","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","checksum":"1f34f3e2cb521033de6154f274ea3a4e","date_updated":"2023-01-20T10:45:06Z"}],"month":"01","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms"},{"month":"05","title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","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.","file":[{"date_created":"2023-06-19T09:37:40Z","access_level":"open_access","creator":"dernst","relation":"main_file","success":1,"date_updated":"2023-06-19T09:37:40Z","file_name":"2023_ElectronCommProbability_Schiavo.pdf","checksum":"4a543fe4b3f9e747cc52167c17bfb524","file_id":"13152","file_size":271434,"content_type":"application/pdf"}],"date_published":"2023-05-05T00:00:00Z","year":"2023","type":"journal_article","article_type":"original","intvolume":"        28","ddc":["510"],"publication":"Electronic Communications in Probability","day":"05","project":[{"grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","name":"Configuration Spaces over Non-Smooth Spaces"}],"publication_identifier":{"eissn":["1083-589X"]},"oa":1,"quality_controlled":"1","publication_status":"published","publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","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."}],"corr_author":"1","citation":{"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>.","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.","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>.","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>","ista":"Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12.","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>","short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12."},"file_date_updated":"2023-06-19T09:37:40Z","author":[{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"last_name":"Lytvynov","full_name":"Lytvynov, Eugene","first_name":"Eugene"}],"volume":28,"external_id":{"isi":["001042025400001"]},"fulldoi":"https://doi.org/10.1214/23-ECP528","oa_version":"Published Version","language":[{"iso":"eng"}],"has_accepted_license":"1","isi":1,"date_created":"2023-06-18T22:00:48Z","_id":"13145","doi":"10.1214/23-ECP528","article_processing_charge":"No","scopus_import":"1","date_updated":"2025-04-14T12:59:08Z","page":"1-12","status":"public","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"department":[{"_id":"JaMa"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"corr_author":"1","citation":{"ista":"Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv, 2309.11292.","short":"L. Dello Schiavo, F. Quattrocchi, ArXiv (n.d.).","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>","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>.","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>.","ieee":"L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a polychromatic Ewens sampling formula,” <i>arXiv</i>. .","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>"},"author":[{"last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"first_name":"Filippo","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","orcid":"0009-0000-9773-1931","full_name":"Quattrocchi, Filippo","last_name":"Quattrocchi"}],"project":[{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F06504","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425"}],"arxiv":1,"oa":1,"publication_status":"draft","type":"preprint","OA_type":"green","publication":"arXiv","day":"20","title":"Multivariate Dirichlet moments and a polychromatic Ewens sampling formula","month":"09","date_published":"2023-09-20T00:00:00Z","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.","year":"2023","OA_place":"repository","status":"public","article_number":"2309.11292","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"_id":"20572","doi":"10.48550/arXiv.2309.11292","article_processing_charge":"No","date_updated":"2025-11-24T13:53:48Z","keyword":["Dirichlet distribution","Ewens sampling formula","Hoppe urn model","colored partitions"],"oa_version":"Preprint","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.11292"}],"date_created":"2025-10-28T13:13:08Z","external_id":{"arxiv":["2309.11292"]},"fulldoi":"https://doi.org/10.48550/arXiv.2309.11292"}]