[{"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."}],"publication_status":"published","language":[{"iso":"eng"}],"status":"public","quality_controlled":"1","citation":{"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>","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","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.","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>.","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>","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>.","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."},"type":"journal_article","article_type":"original","department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"isi":1,"author":[{"orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo"}],"year":"2022","doi":"10.1214/21-AOP1541","arxiv":1,"oa_version":"Preprint","publisher":"Institute of Mathematical Statistics","day":"01","volume":50,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1811.11598"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","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).","intvolume":"        50","oa":1,"scopus_import":"1","date_updated":"2023-10-17T12:50:24Z","title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","month":"03","date_published":"2022-03-01T00:00:00Z","article_processing_charge":"No","ec_funded":1,"publication":"Annals of Probability","page":"591-648","_id":"11354","project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","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"}],"date_created":"2022-05-08T22:01:44Z","external_id":{"arxiv":["1811.11598"],"isi":["000773518500005"]}},{"type":"journal_article","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. 2022;50(3):984-1012. doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” <i>Annals of Probability</i>, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022."},"article_type":"original","publication_status":"published","abstract":[{"text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","doi":"10.1214/21-AOP1552","oa_version":"Preprint","arxiv":1,"publisher":"Institute of Mathematical Statistics","day":"01","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"department":[{"_id":"LaEr"}],"year":"2022","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"isi":1,"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"volume":50,"intvolume":"        50","oa":1,"issue":"3","acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"Annals of Probability","page":"984-1012","_id":"11418","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"date_created":"2022-05-29T22:01:53Z","date_updated":"2023-08-03T07:16:53Z","title":"Normal fluctuation in quantum ergodicity for Wigner matrices","month":"05","article_processing_charge":"No","date_published":"2022-05-01T00:00:00Z"}]