[{"author":[{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","last_name":"Pedrotti","first_name":"Francesco","full_name":"Pedrotti, Francesco"}],"external_id":{"arxiv":["2308.00516"],"isi":["001434322900006"]},"language":[{"iso":"eng"}],"intvolume":"        35","status":"public","page":"196 - 250","title":"Contractive coupling rates and curvature lower bounds for Markov chains","quality_controlled":"1","OA_type":"green","related_material":{"record":[{"id":"17351","relation":"earlier_version","status":"public"}]},"volume":35,"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","corr_author":"1","date_created":"2025-07-21T07:49:15Z","oa":1,"department":[{"_id":"JaMa"}],"citation":{"ista":"Pedrotti F. 2025. Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. 35(1), 196–250.","apa":"Pedrotti, F. (2025). Contractive coupling rates and curvature lower bounds for Markov chains. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/24-aap2113\">https://doi.org/10.1214/24-aap2113</a>","short":"F. Pedrotti, The Annals of Applied Probability 35 (2025) 196–250.","mla":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>The Annals of Applied Probability</i>, vol. 35, no. 1, Institute of Mathematical Statistics, 2025, pp. 196–250, doi:<a href=\"https://doi.org/10.1214/24-aap2113\">10.1214/24-aap2113</a>.","ama":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. <i>The Annals of Applied Probability</i>. 2025;35(1):196-250. doi:<a href=\"https://doi.org/10.1214/24-aap2113\">10.1214/24-aap2113</a>","chicago":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/24-aap2113\">https://doi.org/10.1214/24-aap2113</a>.","ieee":"F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” <i>The Annals of Applied Probability</i>, vol. 35, no. 1. Institute of Mathematical Statistics, pp. 196–250, 2025."},"type":"journal_article","publication_identifier":{"issn":["1050-5164"]},"acknowledgement":"The author warmly thanks Jan Maas for suggesting the project and for his guidance, and Melchior Wirth and Haonan Zhang for useful discussions. The author is also grateful to an anonymous reviewer for carefully reading the manuscript and providing many valuable suggestions. The author gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme\r\n(grant agreement No. 716117) and by the Austrian Science Fund (FWF), Project SFB F65.","doi":"10.1214/24-aap2113","day":"01","_id":"20040","issue":"1","publication":"The Annals of Applied Probability","publisher":"Institute of Mathematical Statistics","date_published":"2025-02-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2308.00516","open_access":"1"}],"year":"2025","scopus_import":"1","abstract":[{"text":"Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincaré inequality) for some classes of Markov chains. In this work, for most of the examples discussed by Conforti, we use contractive coupling rates to prove stronger inequalities, in the form of curvature lower bounds (in entropic and discrete Bakry–Émery sense) and geodesic convexity of some entropic functionals. In addition, we recall and give straightforward generalizations of some notions of coarse Ricci curvature, and we discuss some of their properties and relations with the concepts of couplings and coupling rates: as an application, we show exponential contraction of the p-Wasserstein distance for the heat flow in the aforementioned examples.","lang":"eng"}],"month":"02","isi":1,"arxiv":1,"date_updated":"2025-11-05T13:50:07Z","oa_version":"Preprint","publication_status":"published","OA_place":"repository","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"article_processing_charge":"No"},{"title":"L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model","quality_controlled":"1","page":"1913-1940","intvolume":"        35","status":"public","author":[{"id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","orcid":"0000-0002-6246-1465","last_name":"Khudiakova","first_name":"Kseniia","full_name":"Khudiakova, Kseniia"},{"last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Francesco","full_name":"Pedrotti, Francesco","last_name":"Pedrotti","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"external_id":{"isi":["001523520000012"],"arxiv":["2402.04151"]},"language":[{"iso":"eng"}],"article_type":"original","corr_author":"1","date_created":"2025-07-21T08:13:54Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","related_material":{"record":[{"id":"17352","relation":"earlier_version","status":"public"}]},"volume":35,"OA_type":"green","issue":"3","publication":"The Annals of Applied Probability","_id":"20050","day":"01","publication_identifier":{"issn":["1050-5164"]},"acknowledgement":"This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65 and the Austrian Academy of Science, DOC fellowship nr. 26293.","doi":"10.1214/25-aap2162","oa":1,"citation":{"chicago":"Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-aap2162\">https://doi.org/10.1214/25-aap2162</a>.","ieee":"K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model,” <i>The Annals of Applied Probability</i>, vol. 35, no. 3. Institute of Mathematical Statistics, pp. 1913–1940, 2025.","ista":"Khudiakova K, Maas J, Pedrotti F. 2025. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. The Annals of Applied Probability. 35(3), 1913–1940.","apa":"Khudiakova, K., Maas, J., &#38; Pedrotti, F. (2025). L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-aap2162\">https://doi.org/10.1214/25-aap2162</a>","short":"K. Khudiakova, J. Maas, F. Pedrotti, The Annals of Applied Probability 35 (2025) 1913–1940.","ama":"Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>The Annals of Applied Probability</i>. 2025;35(3):1913-1940. doi:<a href=\"https://doi.org/10.1214/25-aap2162\">10.1214/25-aap2162</a>","mla":"Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>The Annals of Applied Probability</i>, vol. 35, no. 3, Institute of Mathematical Statistics, 2025, pp. 1913–40, doi:<a href=\"https://doi.org/10.1214/25-aap2162\">10.1214/25-aap2162</a>."},"department":[{"_id":"JaMa"}],"type":"journal_article","publication_status":"published","OA_place":"repository","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"The impact of deleterious mutations on small populations","_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293"}],"article_processing_charge":"No","oa_version":"Preprint","year":"2025","abstract":[{"lang":"eng","text":"We prove upper bounds on the L∞-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the L∞-Wasserstein metric and the relative L∞-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic techniques using Langevin dynamics. As an application of these results, we obtain sharp exponential rates of convergence in Fisher’s infinitesimal model from quantitative genetics, generalising recent results by Calvez, Poyato, and Santambrogio in dimension 1 to arbitrary dimensions."}],"scopus_import":"1","month":"06","isi":1,"arxiv":1,"date_updated":"2025-09-30T14:12:48Z","publisher":"Institute of Mathematical Statistics","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.04151"}],"date_published":"2025-06-01T00:00:00Z"},{"_id":"20591","day":"25","file_date_updated":"2025-11-04T07:34:05Z","publication":"Electronic Communications in Probability","oa":1,"department":[{"_id":"JaMa"}],"citation":{"chicago":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>.","ieee":"G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport maps,” <i>Electronic Communications in Probability</i>, vol. 30. Institute of Mathematical Statistics, 2025.","ista":"Brigati G, Pedrotti F. 2025. Heat flow, log-concavity, and Lipschitz transport maps. Electronic Communications in Probability. 30, 71.","apa":"Brigati, G., &#38; Pedrotti, F. (2025). Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>","short":"G. Brigati, F. Pedrotti, Electronic Communications in Probability 30 (2025).","ama":"Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. 2025;30. doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>","mla":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>, vol. 30, 71, Institute of Mathematical Statistics, 2025, doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>."},"type":"journal_article","publication_identifier":{"eissn":["1083-589X"]},"acknowledgement":"This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65 and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. The authors thank Professors Jean Dolbeault, Jan Maas, and Nikita Simonov for many useful comments, and Professors Kazuhiro Ishige, Asuka Takatsu, and Yair Shenfeld for inspiring interactions.","doi":"10.1214/25-ECP717","oa_version":"Published Version","file":[{"success":1,"date_updated":"2025-11-04T07:34:05Z","file_size":278078,"file_name":"2025_ElectronJourProbab_Brigati.pdf","checksum":"67858edbd74658fe38955fa1216f2f18","content_type":"application/pdf","date_created":"2025-11-04T07:34:05Z","relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"20596"}],"OA_place":"publisher","publication_status":"published","article_processing_charge":"Yes","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"publisher":"Institute of Mathematical Statistics","date_published":"2025-09-25T00:00:00Z","year":"2025","scopus_import":"1","abstract":[{"lang":"eng","text":"In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian admits an explicit, uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant of a transport map pushing forward the standard Gaussian to a measure in this class. On the other hand, we show that assuming only fast decay of the tails of the initial datum does not suffice to guarantee uniform log-Hessian upper bounds."}],"isi":1,"month":"09","arxiv":1,"date_updated":"2025-12-01T15:08:54Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"DOAJ_listed":"1","title":"Heat flow, log-concavity, and Lipschitz transport maps","quality_controlled":"1","external_id":{"isi":["001611557000018"],"arxiv":["2404.15205"]},"author":[{"full_name":"Brigati, Giovanni","first_name":"Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1"},{"last_name":"Pedrotti","first_name":"Francesco","full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"language":[{"iso":"eng"}],"intvolume":"        30","status":"public","PlanS_conform":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"71","article_type":"original","corr_author":"1","ddc":["500"],"date_created":"2025-11-02T23:01:35Z","has_accepted_license":"1","OA_type":"gold","related_material":{"record":[{"id":"17353","status":"public","relation":"earlier_version"}]},"volume":30,"ec_funded":1},{"publication_status":"published","OA_place":"publisher","article_processing_charge":"No","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"oa_version":"Published Version","file":[{"access_level":"open_access","creator":"dernst","date_created":"2025-01-27T12:19:44Z","relation":"main_file","file_id":"18898","file_size":780315,"date_updated":"2025-01-27T12:19:44Z","success":1,"content_type":"application/pdf","file_name":"2024_TMLR_Pedrotti.pdf","checksum":"76a1fd5afd8ee6f7ae0e5912d7dbf6b4"}],"alternative_title":["TMLR"],"scopus_import":"1","year":"2024","abstract":[{"lang":"eng","text":"Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time T1 by adding noise to the data, (ii) estimate its score function, and (iii) use such estimate to run a reverse process. As the reverse process is initialized with the stationary distribution of the forward one, the existing analysis paradigm requires T1→∞. This is however problematic: from a theoretical viewpoint, for a given precision of the score approximation, the convergence guarantee fails as T1 diverges; from a practical viewpoint, a large T1 increases computational costs and leads to error propagation. This paper addresses the issue by considering a version of the popular predictor-corrector scheme: after running the forward process, we first estimate the final distribution via an inexact Langevin dynamics and then revert the process. Our key technical contribution is to provide convergence guarantees which require to run the forward process only for a fixed finite time T1. Our bounds exhibit a mild logarithmic dependence on the input dimension and the subgaussian norm of the target distribution, have minimal assumptions on the data, and require only to control the L2 loss on the score approximation, which is the quantity minimized in practice."}],"date_updated":"2025-04-15T08:31:35Z","arxiv":1,"month":"06","date_published":"2024-06-01T00:00:00Z","file_date_updated":"2025-01-27T12:19:44Z","publication":"Transactions on Machine Learning Research","_id":"18897","day":"01","acknowledgement":"Francesco Pedrotti and Jan Maas acknowledge support by the Austrian Science Fund (FWF) project 10.55776/F65. Marco Mondelli acknowledges support by the 2019 Lopez-Loreta prize.\r\n","publication_identifier":{"issn":["2835-8856"]},"oa":1,"department":[{"_id":"JaMa"},{"_id":"MaMo"}],"type":"conference","citation":{"short":"F. Pedrotti, J. Maas, M. Mondelli, in:, Transactions on Machine Learning Research, 2024.","ama":"Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. In: <i>Transactions on Machine Learning Research</i>. ; 2024.","mla":"Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” <i>Transactions on Machine Learning Research</i>, 2024.","apa":"Pedrotti, F., Maas, J., &#38; Mondelli, M. (2024). Improved convergence of score-based diffusion models via prediction-correction. In <i>Transactions on Machine Learning Research</i>.","ista":"Pedrotti F, Maas J, Mondelli M. 2024. Improved convergence of score-based diffusion models via prediction-correction. Transactions on Machine Learning Research. , TMLR, .","ieee":"F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based diffusion models via prediction-correction,” in <i>Transactions on Machine Learning Research</i>, 2024.","chicago":"Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” In <i>Transactions on Machine Learning Research</i>, 2024."},"corr_author":"1","date_created":"2025-01-27T12:18:05Z","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"17350","status":"public","relation":"earlier_version"}]},"has_accepted_license":"1","OA_type":"gold","quality_controlled":"1","title":"Improved convergence of score-based diffusion models via prediction-correction","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","language":[{"iso":"eng"}],"author":[{"last_name":"Pedrotti","full_name":"Pedrotti, Francesco","first_name":"Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"},{"first_name":"Jan","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"27EB676C-8706-11E9-9510-7717E6697425","full_name":"Mondelli, Marco","first_name":"Marco","last_name":"Mondelli","orcid":"0000-0002-3242-7020"}],"external_id":{"arxiv":["2305.14164"]}},{"corr_author":"1","ddc":["500","510","515","519"],"date_created":"2024-07-29T09:14:14Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","related_material":{"record":[{"id":"17351","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"17353"},{"id":"17350","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"17352"},{"relation":"part_of_dissertation","status":"public","id":"17143"}]},"ec_funded":1,"has_accepted_license":"1","title":"Functional inequalities and convergence of stochastic processes","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"page":"183","supervisor":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338"}],"status":"public","author":[{"full_name":"Pedrotti, Francesco","first_name":"Francesco","last_name":"Pedrotti","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"language":[{"iso":"eng"}],"publication_status":"published","OA_place":"publisher","article_processing_charge":"No","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"oa_version":"Published Version","file":[{"creator":"fpedrott","access_level":"open_access","relation":"main_file","date_created":"2024-08-02T09:23:26Z","file_id":"17366","file_size":2941599,"date_updated":"2024-08-02T09:23:26Z","success":1,"content_type":"application/pdf","checksum":"11650bab714ef85ad43a287060850523","file_name":"thesis_final.pdf"},{"content_type":"application/x-zip-compressed","checksum":"c30ba5611941226cf1bfc867c25b1e80","file_name":"thesis_final_source.zip","file_size":6293375,"date_updated":"2024-08-02T09:27:15Z","file_id":"17367","creator":"fpedrott","access_level":"closed","relation":"source_file","date_created":"2024-08-02T09:27:15Z"}],"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"}],"year":"2024","alternative_title":["ISTA Thesis"],"month":"07","date_updated":"2026-04-07T13:00:03Z","publisher":"Institute of Science and Technology Austria","date_published":"2024-07-31T00:00:00Z","file_date_updated":"2024-08-02T09:27:15Z","day":"31","_id":"17336","publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","doi":"10.15479/at:ista:17336","oa":1,"type":"dissertation","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"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>","ista":"Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria.","short":"F. Pedrotti, Functional Inequalities and Convergence of Stochastic Processes, Institute of Science and Technology Austria, 2024.","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>.","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>","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>.","ieee":"F. Pedrotti, “Functional inequalities and convergence of stochastic processes,” Institute of Science and Technology Austria, 2024."}},{"arxiv":1,"date_updated":"2026-04-07T13:00:02Z","month":"06","isi":1,"year":"2024","scopus_import":"1","abstract":[{"lang":"eng","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."}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.05239","open_access":"1"}],"date_published":"2024-06-01T00:00:00Z","publisher":"American Mathematical Society","article_processing_charge":"No","project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"publication_status":"published","oa_version":"Preprint","doi":"10.1090/tran/9156","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","publication_identifier":{"issn":["0002-9947"],"eissn":["1088-6850"]},"citation":{"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.","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>.","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.","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>"},"type":"journal_article","department":[{"_id":"JaMa"}],"oa":1,"publication":"Transactions of the American Mathematical Society","issue":"6","_id":"17143","day":"01","ec_funded":1,"volume":377,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"17336"}]},"date_created":"2024-06-16T22:01:06Z","article_type":"original","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","intvolume":"       377","language":[{"iso":"eng"}],"author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","orcid":"0000-0002-0845-1338","first_name":"Jan","full_name":"Maas, Jan"},{"first_name":"Francesco","full_name":"Pedrotti, Francesco","last_name":"Pedrotti","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"external_id":{"isi":["001203273300001"],"arxiv":["2304.05239"]},"quality_controlled":"1","title":"Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces","page":"3779-3804"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","article_processing_charge":"No","date_created":"2024-07-31T07:56:40Z","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"publication_status":"draft","corr_author":"1","OA_place":"repository","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2305.14164"}],"date_published":"2024-06-06T00:00:00Z","arxiv":1,"date_updated":"2026-04-07T13:00:02Z","month":"06","year":"2024","related_material":{"record":[{"id":"18897","status":"public","relation":"later_version"},{"id":"17336","relation":"dissertation_contains","status":"public"}]},"abstract":[{"lang":"eng","text":"Score-based generative models (SGMs) are powerful tools to sample from\r\ncomplex data distributions. Their underlying idea is to (i) run a forward\r\nprocess for time $T_1$ by adding noise to the data, (ii) estimate its score\r\nfunction, and (iii) use such estimate to run a reverse process. As the reverse\r\nprocess is initialized with the stationary distribution of the forward one, the\r\nexisting analysis paradigm requires $T_1\\to\\infty$. This is however\r\nproblematic: from a theoretical viewpoint, for a given precision of the score\r\napproximation, the convergence guarantee fails as $T_1$ diverges; from a\r\npractical viewpoint, a large $T_1$ increases computational costs and leads to\r\nerror propagation. This paper addresses the issue by considering a version of\r\nthe popular predictor-corrector scheme: after running the forward process, we\r\nfirst estimate the final distribution via an inexact Langevin dynamics and then\r\nrevert the process. Our key technical contribution is to provide convergence\r\nguarantees which require to run the forward process only for a fixed finite\r\ntime $T_1$. Our bounds exhibit a mild logarithmic dependence on the input\r\ndimension and the subgaussian norm of the target distribution, have minimal\r\nassumptions on the data, and require only to control the $L^2$ loss on the\r\nscore approximation, which is the quantity minimized in practice."}],"_id":"17350","day":"06","publication":"arXiv","title":"Improved convergence of score-based diffusion models via prediction-correction","department":[{"_id":"JaMa"},{"_id":"MaMo"}],"citation":{"short":"F. Pedrotti, J. Maas, M. Mondelli, ArXiv (n.d.).","mla":"Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2305.14164\">10.48550/arXiv.2305.14164</a>.","ama":"Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2305.14164\">10.48550/arXiv.2305.14164</a>","ista":"Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2305.14164\">10.48550/arXiv.2305.14164</a>.","apa":"Pedrotti, F., Maas, J., &#38; Mondelli, M. (n.d.). Improved convergence of score-based diffusion models via prediction-correction. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2305.14164\">https://doi.org/10.48550/arXiv.2305.14164</a>","ieee":"F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based diffusion models via prediction-correction,” <i>arXiv</i>. .","chicago":"Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2305.14164\">https://doi.org/10.48550/arXiv.2305.14164</a>."},"type":"preprint","oa":1,"language":[{"iso":"eng"}],"author":[{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","last_name":"Pedrotti","full_name":"Pedrotti, Francesco","first_name":"Francesco"},{"first_name":"Jan","full_name":"Maas, Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Marco","full_name":"Mondelli, Marco","last_name":"Mondelli","orcid":"0000-0002-3242-7020","id":"27EB676C-8706-11E9-9510-7717E6697425"}],"external_id":{"arxiv":["2305.14164"]},"status":"public","doi":"10.48550/arXiv.2305.14164"},{"_id":"17352","day":"07","title":"L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model","publication":"arXiv","external_id":{"arxiv":["2402.04151"]},"author":[{"orcid":"0000-0002-6246-1465","last_name":"Khudiakova","full_name":"Khudiakova, Kseniia","first_name":"Kseniia","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","first_name":"Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"},{"id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","full_name":"Pedrotti, Francesco","first_name":"Francesco","last_name":"Pedrotti"}],"oa":1,"language":[{"iso":"eng"}],"type":"preprint","department":[{"_id":"JaMa"}],"citation":{"short":"K. Khudiakova, J. Maas, F. Pedrotti, ArXiv (n.d.).","ama":"Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2402.04151\">10.48550/arXiv.2402.04151</a>","mla":"Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>ArXiv</i>, 2402.04151, doi:<a href=\"https://doi.org/10.48550/arXiv.2402.04151\">10.48550/arXiv.2402.04151</a>.","apa":"Khudiakova, K., Maas, J., &#38; Pedrotti, F. (n.d.). L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2402.04151\">https://doi.org/10.48550/arXiv.2402.04151</a>","ista":"Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. arXiv, 2402.04151.","ieee":"K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model,” <i>arXiv</i>. .","chicago":"Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2402.04151\">https://doi.org/10.48550/arXiv.2402.04151</a>."},"doi":"10.48550/arXiv.2402.04151","status":"public","article_number":"2402.04151","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"repository","publication_status":"draft","corr_author":"1","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"The impact of deleterious mutations on small populations","_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293"}],"article_processing_charge":"No","date_created":"2024-07-31T08:07:40Z","date_published":"2024-02-07T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2402.04151","open_access":"1"}],"year":"2024","related_material":{"record":[{"id":"20050","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"17336"}]},"abstract":[{"lang":"eng","text":"We prove upper bounds on the $L^\\infty$-Wasserstein distance from optimal\r\ntransport between strongly log-concave probability densities and log-Lipschitz\r\nperturbations. In the simplest setting, such a bound amounts to a\r\ntransport-information inequality involving the $L^\\infty$-Wasserstein metric\r\nand the relative $L^\\infty$-Fisher information. We show that this inequality\r\ncan be sharpened significantly in situations where the involved densities are\r\nanisotropic. Our proof is based on probabilistic techniques using Langevin\r\ndynamics. As an application of these results, we obtain sharp exponential rates\r\nof convergence in Fisher's infinitesimal model from quantitative genetics,\r\ngeneralising recent results by Calvez, Poyato, and Santambrogio in dimension 1\r\nto arbitrary dimensions."}],"month":"02","arxiv":1,"date_updated":"2026-04-07T13:00:02Z"},{"article_number":"2404.15205","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2024-07-31T08:17:14Z","OA_place":"repository","corr_author":"1","publication_status":"draft","date_published":"2024-05-08T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2404.15205","open_access":"1"}],"date_updated":"2026-04-07T13:00:02Z","arxiv":1,"month":"05","abstract":[{"text":"In this paper we derive estimates for the Hessian of the logarithm\r\n(log-Hessian) for solutions to the heat equation. For initial data in the form\r\nof log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian\r\nadmits an explicit, uniform (in space) lower bound. This yields a new estimate\r\nfor the Lipschitz constant of a transport map pushing forward the standard\r\nGaussian to a measure in this class. Further connections are discussed with\r\nscore-based diffusion models and improved Gaussian logarithmic Sobolev\r\ninequalities. Finally, we show that assuming only fast decay of the tails of\r\nthe initial datum does not suffice to guarantee uniform log-Hessian upper\r\nbounds.","lang":"eng"}],"related_material":{"record":[{"id":"20591","status":"public","relation":"later_version"},{"id":"17336","status":"public","relation":"dissertation_contains"}]},"year":"2024","day":"08","_id":"17353","publication":"arXiv","title":"Heat flow, log-concavity, and Lipschitz transport maps","department":[{"_id":"JaMa"}],"citation":{"ieee":"G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport maps,” <i>arXiv</i>. .","chicago":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2404.15205\">https://doi.org/10.48550/arXiv.2404.15205</a>.","short":"G. Brigati, F. Pedrotti, ArXiv (n.d.).","mla":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>ArXiv</i>, 2404.15205, doi:<a href=\"https://doi.org/10.48550/arXiv.2404.15205\">10.48550/arXiv.2404.15205</a>.","ama":"Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2404.15205\">10.48550/arXiv.2404.15205</a>","apa":"Brigati, G., &#38; Pedrotti, F. (n.d.). Heat flow, log-concavity, and Lipschitz transport maps. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2404.15205\">https://doi.org/10.48550/arXiv.2404.15205</a>","ista":"Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. arXiv, 2404.15205."},"type":"preprint","oa":1,"language":[{"iso":"eng"}],"author":[{"full_name":"Brigati, Giovanni","first_name":"Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1"},{"first_name":"Francesco","full_name":"Pedrotti, Francesco","last_name":"Pedrotti","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"external_id":{"arxiv":["2404.15205"]},"status":"public","doi":"10.48550/arXiv.2404.15205"},{"article_number":"2308.00516","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","OA_place":"repository","corr_author":"1","publication_status":"draft","date_created":"2024-07-31T08:02:16Z","article_processing_charge":"No","date_published":"2023-08-02T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2308.00516"}],"year":"2023","related_material":{"record":[{"relation":"later_version","status":"public","id":"20040"},{"id":"17336","status":"public","relation":"dissertation_contains"}]},"abstract":[{"lang":"eng","text":"Contractive coupling rates have been recently introduced by Conforti as a\r\ntool to establish convex Sobolev inequalities (including modified log-Sobolev\r\nand Poincar\\'{e} inequality) for some classes of Markov chains. In this work,\r\nwe show how contractive coupling rates can also be used to prove stronger\r\ninequalities, in the form of curvature lower bounds for Markov chains and\r\ngeodesic convexity of entropic functionals. We illustrate this in several\r\nexamples discussed by Conforti, where in particular, after appropriately\r\nchoosing a parameter function, we establish positive curvature in the entropic\r\nand (discrete) Bakry--\\'{E}mery sense. In addition, we recall and give\r\nstraightforward generalizations of some notions of coarse Ricci curvature, and\r\nwe discuss some of their properties and relations with the concepts of\r\ncouplings and coupling rates: as an application, we show exponential\r\ncontraction of the $p$-Wasserstein distance for the heat flow in the\r\naforementioned examples."}],"arxiv":1,"date_updated":"2026-04-07T13:00:02Z","month":"08","_id":"17351","day":"02","publication":"arXiv","title":"Contractive coupling rates and curvature lower bounds for Markov chains","oa":1,"language":[{"iso":"eng"}],"author":[{"full_name":"Pedrotti, Francesco","first_name":"Francesco","last_name":"Pedrotti","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"external_id":{"arxiv":["2308.00516"]},"department":[{"_id":"JaMa"}],"citation":{"short":"F. Pedrotti, ArXiv (n.d.).","mla":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>ArXiv</i>, 2308.00516, doi:<a href=\"https://doi.org/10.48550/arXiv.2308.00516\">10.48550/arXiv.2308.00516</a>.","ama":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2308.00516\">10.48550/arXiv.2308.00516</a>","ista":"Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. arXiv, 2308.00516.","apa":"Pedrotti, F. (n.d.). Contractive coupling rates and curvature lower bounds for Markov chains. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2308.00516\">https://doi.org/10.48550/arXiv.2308.00516</a>","ieee":"F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” <i>arXiv</i>. .","chicago":"Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2308.00516\">https://doi.org/10.48550/arXiv.2308.00516</a>."},"type":"preprint","doi":"10.48550/arXiv.2308.00516","status":"public"}]