{"degree_awarded":"PhD","author":[{"first_name":"Francesco","last_name":"Pedrotti","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco"}],"ddc":["500","510","515","519"],"publication_identifier":{"issn":["2663-337X"]},"abstract":[{"lang":"eng","text":"This thesis deals with the study of stochastic processes and their ergodicity properties. The\r\nvariety of problems encountered calls for a set of different approaches, ranging from classical to\r\nmodern ones: a special place is held by probabilistic methods based on couplings, by functional\r\ninequalities, and by the theory of gradient flows in the space of measures.\r\n\r\nThe material is organized as follows. Chapter 1 contains the introduction to this thesis, starting\r\nwith a general presentation of some of the relevant topics. Section 1.1 is dedicated to the\r\ntheory of gradient flows in metric spaces, and introduces the first contribution of this thesis\r\n[DSMP24], which is presented in detail in Chapter 2. Section 1.2 moves to the topic of\r\ncurvature of Markov chains, concluding with a brief description of our second contribution\r\n[Ped23], which is included in Chapter 3. Section 1.3 discusses applications of stochastic\r\nprocesses to the theory of sampling, in particular the recent framework of score-based diffusion\r\nmodels, and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses\r\nsome related problems, concerning the regularization properties of the heat flow. It serves\r\nas a motivation for the work [BP24], which we report in Chapter 5. Finally, Section 1.5\r\ndiscusses the last contribution of this thesis, which can be found in Chapter 6. It deals with\r\nthe convergence to equilibrium of a particular stochastic model from quantitative genetics:\r\nthis is established via some functional inequalities, which we prove with probabilistic arguments\r\nbased on couplings.\r\n"}],"fulldoi":"https://doi.org/10.15479/at:ista:17336","related_material":{"record":[{"relation":"part_of_dissertation","id":"17351","status":"public"},{"id":"17353","relation":"part_of_dissertation","status":"public"},{"id":"17350","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"17352"},{"id":"17143","status":"public","relation":"part_of_dissertation"}]},"file":[{"date_updated":"2024-08-02T09:23:26Z","file_size":2941599,"checksum":"11650bab714ef85ad43a287060850523","success":1,"creator":"fpedrott","content_type":"application/pdf","file_id":"17366","access_level":"open_access","date_created":"2024-08-02T09:23:26Z","relation":"main_file","file_name":"thesis_final.pdf"},{"checksum":"c30ba5611941226cf1bfc867c25b1e80","file_size":6293375,"date_updated":"2024-08-02T09:27:15Z","relation":"source_file","file_name":"thesis_final_source.zip","date_created":"2024-08-02T09:27:15Z","creator":"fpedrott","content_type":"application/x-zip-compressed","file_id":"17367","access_level":"closed"}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","OA_place":"publisher","date_created":"2024-07-29T09:14:14Z","corr_author":"1","date_updated":"2026-04-07T13:00:03Z","date_published":"2024-07-31T00:00:00Z","_id":"17336","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"month":"07","status":"public","title":"Functional inequalities and convergence of stochastic processes","oa":1,"page":"183","file_date_updated":"2024-08-02T09:27:15Z","day":"31","oa_version":"Published Version","supervisor":[{"first_name":"Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan"}],"alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publication_status":"published","publisher":"Institute of Science and Technology Austria","ec_funded":1,"doi":"10.15479/at:ista:17336","type":"dissertation","year":"2024","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"article_processing_charge":"No","citation":{"apa":"Pedrotti, F. (2024). <i>Functional inequalities and convergence of stochastic processes</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17336\">https://doi.org/10.15479/at:ista:17336</a>","chicago":"Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic Processes.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17336\">https://doi.org/10.15479/at:ista:17336</a>.","short":"F. Pedrotti, Functional Inequalities and Convergence of Stochastic Processes, Institute of Science and Technology Austria, 2024.","ieee":"F. Pedrotti, “Functional inequalities and convergence of stochastic processes,” Institute of Science and Technology Austria, 2024.","ama":"Pedrotti F. Functional inequalities and convergence of stochastic processes. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17336\">10.15479/at:ista:17336</a>","mla":"Pedrotti, Francesco. <i>Functional Inequalities and Convergence of Stochastic Processes</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17336\">10.15479/at:ista:17336</a>.","ista":"Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria."}}