[{"publisher":"Springer Nature","department":[{"_id":"JaMa"}],"status":"public","title":"A discovery tour in random Riemannian geometry","publication_status":"epub_ahead","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.","_id":"14934","year":"2024","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","date_updated":"2024-02-05T13:04:23Z","date_created":"2024-02-04T23:00:54Z","author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870"},{"last_name":"Kopfer","first_name":"Eva","full_name":"Kopfer, Eva"},{"first_name":"Karl Theodor","last_name":"Sturm","full_name":"Sturm, Karl Theodor"}],"type":"journal_article","abstract":[{"lang":"eng","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."}],"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"quality_controlled":"1","article_type":"original","citation":{"mla":"Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis, Springer Nature, 2024, doi:10.1007/s11118-023-10118-0.","short":"L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024).","chicago":"Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature, 2024. https://doi.org/10.1007/s11118-023-10118-0.","ama":"Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian geometry. Potential Analysis. 2024. doi:10.1007/s11118-023-10118-0","ista":"Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis.","ieee":"L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” Potential Analysis. Springer Nature, 2024.","apa":"Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0"},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11118-023-10118-0"}],"publication":"Potential Analysis","language":[{"iso":"eng"}],"date_published":"2024-01-26T00:00:00Z","doi":"10.1007/s11118-023-10118-0","scopus_import":"1","publication_identifier":{"eissn":["1572-929X"],"issn":["0926-2601"]},"article_processing_charge":"Yes (via OA deal)","month":"01","day":"26"},{"month":"01","publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"quality_controlled":"1","isi":1,"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208"},{"name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"external_id":{"isi":["000906214600004"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00028-022-00859-7","article_number":"9","license":"https://creativecommons.org/licenses/by/4.0/","file_date_updated":"2023-01-20T10:45:06Z","ec_funded":1,"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"JaMa"}],"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).","year":"2023","date_updated":"2023-06-28T11:54:35Z","date_created":"2023-01-08T23:00:53Z","volume":23,"author":[{"last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo"},{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","first_name":"Melchior","last_name":"Wirth"}],"scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","article_type":"original","publication":"Journal of Evolution Equations","citation":{"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,” Journal of Evolution Equations, vol. 23, no. 1. Springer Nature, 2023.","apa":"Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. Springer Nature. https://doi.org/10.1007/s00028-022-00859-7","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations. Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23, no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023)."},"date_published":"2023-01-01T00:00:00Z","type":"journal_article","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."}],"issue":"1","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","status":"public","ddc":["510"],"intvolume":" 23","_id":"12104","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"success":1,"checksum":"1f34f3e2cb521033de6154f274ea3a4e","date_created":"2023-01-20T10:45:06Z","date_updated":"2023-01-20T10:45:06Z","file_id":"12325","relation":"main_file","creator":"dernst","file_size":422612,"content_type":"application/pdf","access_level":"open_access","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf"}]},{"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2023-03-01T00:00:00Z","page":"573-615","article_type":"original","citation":{"ama":"Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y","ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615, 2023.","apa":"Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y","ista":"Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.","short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.","mla":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature, 2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.","chicago":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis. Springer Nature, 2023. https://doi.org/10.1007/s11118-021-09951-y."},"publication":"Potential Analysis","abstract":[{"lang":"eng","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."}],"type":"journal_article","oa_version":"Published Version","file":[{"file_size":806391,"content_type":"application/pdf","creator":"dernst","file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf","access_level":"open_access","date_updated":"2023-10-04T09:18:59Z","date_created":"2023-10-04T09:18:59Z","checksum":"625526482be300ca7281c91c30d41725","success":1,"relation":"main_file","file_id":"14387"}],"intvolume":" 58","title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","status":"public","ddc":["510"],"_id":"10145","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1572-929X"],"issn":["0926-2601"]},"month":"03","language":[{"iso":"eng"}],"doi":"10.1007/s11118-021-09951-y","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"isi":1,"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2003.01366"],"isi":["000704213400001"]},"ec_funded":1,"file_date_updated":"2023-10-04T09:18:59Z","volume":58,"date_created":"2021-10-17T22:01:17Z","date_updated":"2023-10-04T09:19:12Z","author":[{"full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","first_name":"Lorenzo"}],"publisher":"Springer Nature","department":[{"_id":"JaMa"}],"publication_status":"published","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.","year":"2023"},{"intvolume":" 28","status":"public","title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","ddc":["510"],"_id":"13145","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_name":"2023_ElectronCommProbability_Schiavo.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":271434,"file_id":"13152","relation":"main_file","date_updated":"2023-06-19T09:37:40Z","date_created":"2023-06-19T09:37:40Z","success":1,"checksum":"4a543fe4b3f9e747cc52167c17bfb524"}],"oa_version":"Published Version","type":"journal_article","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."}],"page":"1-12","article_type":"original","citation":{"chicago":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528.","short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12.","mla":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528.","apa":"Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528","ieee":"L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” Electronic Communications in Probability, 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.","ama":"Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528"},"publication":"Electronic Communications in Probability","date_published":"2023-05-05T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"No","day":"05","department":[{"_id":"JaMa"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","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.","year":"2023","volume":28,"date_updated":"2023-12-13T11:24:57Z","date_created":"2023-06-18T22:00:48Z","author":[{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"last_name":"Lytvynov","first_name":"Eugene","full_name":"Lytvynov, Eugene"}],"file_date_updated":"2023-06-19T09:37:40Z","project":[{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"}],"isi":1,"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["001042025400001"]},"language":[{"iso":"eng"}],"doi":"10.1214/23-ECP528","publication_identifier":{"eissn":["1083-589X"]},"month":"05"},{"month":"11","publication_identifier":{"issn":["2330-1511"]},"tmp":{"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)","image":"/images/cc_by_nc_nd.png"},"oa":1,"quality_controlled":"1","project":[{"_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"}],"doi":"10.1090/bproc/134","language":[{"iso":"eng"}],"file_date_updated":"2023-01-26T13:02:07Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","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.","year":"2022","publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"American Mathematical Society","author":[{"first_name":"Tommaso","last_name":"Cremaschi","full_name":"Cremaschi, Tommaso"},{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"date_created":"2023-01-12T12:12:17Z","date_updated":"2023-01-26T13:04:13Z","volume":9,"scopus_import":"1","day":"02","article_processing_charge":"No","has_accepted_license":"1","publication":"Proceedings of the American Mathematical Society, Series B","citation":{"ama":"Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 2022;9(43):445-459. doi:10.1090/bproc/134","ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.","apa":"Cremaschi, T., & Dello Schiavo, L. (2022). Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. American Mathematical Society. https://doi.org/10.1090/bproc/134","ieee":"T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43. American Mathematical Society, pp. 445–459, 2022.","mla":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134.","short":"T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459.","chicago":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B. American Mathematical Society, 2022. https://doi.org/10.1090/bproc/134."},"article_type":"original","page":"445-459","date_published":"2022-11-02T00:00:00Z","type":"journal_article","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."}],"issue":"43","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12177","title":"Effective contraction of Skinning maps","ddc":["510"],"status":"public","intvolume":" 9","oa_version":"Published Version","file":[{"checksum":"cb4a79937c1f60d4c329a10ee797f0d2","success":1,"date_updated":"2023-01-26T13:02:07Z","date_created":"2023-01-26T13:02:07Z","relation":"main_file","file_id":"12404","content_type":"application/pdf","file_size":326471,"creator":"dernst","access_level":"open_access","file_name":"2022_ProceedingsAMS_Cremaschi.pdf"}]},{"month":"12","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"doi":"10.1007/s00208-021-02331-2","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000734150200001"],"arxiv":["2110.05137"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"file_date_updated":"2022-01-03T11:08:31Z","ec_funded":1,"author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870"},{"first_name":"Kohei","last_name":"Suzuki","full_name":"Suzuki, Kohei"}],"date_updated":"2023-08-02T13:39:05Z","date_created":"2022-01-02T23:01:35Z","volume":384,"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.","year":"2022","publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"Springer Nature","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"date_published":"2022-12-01T00:00:00Z","publication":"Mathematische Annalen","citation":{"short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature, 2022. https://doi.org/10.1007/s00208-021-02331-2.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2","ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp. 1815–1832, 2022.","apa":"Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832."},"article_type":"original","page":"1815-1832","abstract":[{"lang":"eng","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."}],"type":"journal_article","file":[{"file_id":"10596","relation":"main_file","success":1,"checksum":"2593abbf195e38efa93b6006b1e90eb1","date_updated":"2022-01-03T11:08:31Z","date_created":"2022-01-03T11:08:31Z","access_level":"open_access","file_name":"2021_MathAnn_DelloSchiavo.pdf","creator":"alisjak","content_type":"application/pdf","file_size":410090}],"oa_version":"Published Version","_id":"10588","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","ddc":["510"],"title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","intvolume":" 384"},{"scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Annals of Probability","citation":{"apa":"Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” Annals of Probability, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","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.","ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648. doi:10.1214/21-AOP1541","chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.","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.” Annals of Probability, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541."},"article_type":"original","page":"591-648","date_published":"2022-03-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","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."}],"issue":"2","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"11354","status":"public","title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","intvolume":" 50","oa_version":"Preprint","month":"03","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"external_id":{"arxiv":["1811.11598"],"isi":["000773518500005"]},"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1811.11598","open_access":"1"}],"oa":1,"isi":1,"quality_controlled":"1","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"doi":"10.1214/21-AOP1541","language":[{"iso":"eng"}],"ec_funded":1,"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).","year":"2022","publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"Institute of Mathematical Statistics","author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870"}],"date_created":"2022-05-08T22:01:44Z","date_updated":"2023-10-17T12:50:24Z","volume":50},{"day":"15","article_processing_charge":"No","scopus_import":"1","date_published":"2021-09-15T00:00:00Z","article_type":"original","publication":"Journal of Functional Analysis","citation":{"ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 2021;281(11). doi:10.1016/j.jfa.2021.109234","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.","apa":"Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109234","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” Journal of Functional Analysis, vol. 281, no. 11. Elsevier, 2021.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis, vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234.","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109234."},"abstract":[{"lang":"eng","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."}],"issue":"11","type":"journal_article","oa_version":"Preprint","title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","status":"public","intvolume":" 281","_id":"10070","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"09","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.jfa.2021.109234","isi":1,"quality_controlled":"1","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2008.01492"}],"oa":1,"external_id":{"isi":["000703896600005"],"arxiv":["2008.01492"]},"ec_funded":1,"article_number":"109234","date_updated":"2023-08-14T07:05:44Z","date_created":"2021-10-03T22:01:21Z","volume":281,"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo"},{"full_name":"Suzuki, Kohei","last_name":"Suzuki","first_name":"Kohei"}],"publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"Elsevier","year":"2021","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."}]