{"title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","status":"public","ec_funded":1,"month":"03","type":"journal_article","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","article_type":"original","date_created":"2022-05-08T22:01:44Z","oa_version":"Preprint","date_published":"2022-03-01T00:00:00Z","scopus_import":"1","quality_controlled":"1","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."}],"project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"author":[{"orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo"}],"intvolume":"        50","citation":{"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>.","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>","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.","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. <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>","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648."},"isi":1,"department":[{"_id":"JaMa"}],"publication_status":"published","external_id":{"isi":["000773518500005"],"arxiv":["1811.11598"]},"volume":50,"year":"2022","publisher":"Institute of Mathematical Statistics","day":"01","oa":1,"language":[{"iso":"eng"}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1811.11598","open_access":"1"}],"date_updated":"2023-10-17T12:50:24Z","publication":"Annals of Probability","_id":"11354","issue":"2","doi":"10.1214/21-AOP1541","page":"591-648","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)."}