--- OA_place: repository OA_type: green _id: '20040' abstract: - lang: eng 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.' 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." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. 2025;35(1):196-250. doi:10.1214/24-aap2113 apa: Pedrotti, F. (2025). Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/24-aap2113 chicago: Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/24-aap2113. ieee: F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” The Annals of Applied Probability, vol. 35, no. 1. Institute of Mathematical Statistics, pp. 196–250, 2025. ista: Pedrotti F. 2025. Contractive coupling rates and curvature lower bounds for Markov chains. The Annals of Applied Probability. 35(1), 196–250. mla: Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” The Annals of Applied Probability, vol. 35, no. 1, Institute of Mathematical Statistics, 2025, pp. 196–250, doi:10.1214/24-aap2113. short: F. Pedrotti, The Annals of Applied Probability 35 (2025) 196–250. corr_author: '1' date_created: 2025-07-21T07:49:15Z date_published: 2025-02-01T00:00:00Z date_updated: 2025-11-05T13:50:07Z day: '01' department: - _id: JaMa doi: 10.1214/24-aap2113 ec_funded: 1 external_id: arxiv: - '2308.00516' isi: - '001434322900006' intvolume: ' 35' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2308.00516 month: '02' oa: 1 oa_version: Preprint page: 196 - 250 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: The Annals of Applied Probability publication_identifier: issn: - 1050-5164 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' related_material: record: - id: '17351' relation: earlier_version status: public scopus_import: '1' status: public title: Contractive coupling rates and curvature lower bounds for Markov chains type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 35 year: '2025' ... --- OA_place: repository OA_type: green _id: '20050' 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. 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Kseniia full_name: Khudiakova, Kseniia id: 4E6DC800-AE37-11E9-AC72-31CAE5697425 last_name: Khudiakova orcid: 0000-0002-6246-1465 - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. The Annals of Applied Probability. 2025;35(3):1913-1940. doi:10.1214/25-aap2162 apa: 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. Institute of Mathematical Statistics. https://doi.org/10.1214/25-aap2162 chicago: Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/25-aap2162. ieee: K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model,” The Annals of Applied Probability, 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. mla: Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” The Annals of Applied Probability, vol. 35, no. 3, Institute of Mathematical Statistics, 2025, pp. 1913–40, doi:10.1214/25-aap2162. short: K. Khudiakova, J. Maas, F. Pedrotti, The Annals of Applied Probability 35 (2025) 1913–1940. corr_author: '1' date_created: 2025-07-21T08:13:54Z date_published: 2025-06-01T00:00:00Z date_updated: 2025-09-30T14:12:48Z day: '01' department: - _id: JaMa doi: 10.1214/25-aap2162 external_id: arxiv: - '2402.04151' isi: - '001523520000012' intvolume: ' 35' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2402.04151 month: '06' oa: 1 oa_version: Preprint page: 1913-1940 project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8 grant_number: '26293' name: The impact of deleterious mutations on small populations publication: The Annals of Applied Probability publication_identifier: issn: - 1050-5164 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' related_material: record: - id: '17352' relation: earlier_version status: public scopus_import: '1' status: public title: L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 35 year: '2025' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: gold PlanS_conform: '1' _id: '20591' 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. 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. article_number: '71' article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Giovanni full_name: Brigati, Giovanni id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1 last_name: Brigati - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. Electronic Communications in Probability. 2025;30. doi:10.1214/25-ECP717 apa: Brigati, G., & Pedrotti, F. (2025). Heat flow, log-concavity, and Lipschitz transport maps. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-ECP717 chicago: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/25-ECP717. ieee: G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport maps,” Electronic Communications in Probability, 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. mla: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” Electronic Communications in Probability, vol. 30, 71, Institute of Mathematical Statistics, 2025, doi:10.1214/25-ECP717. short: G. Brigati, F. Pedrotti, Electronic Communications in Probability 30 (2025). corr_author: '1' date_created: 2025-11-02T23:01:35Z date_published: 2025-09-25T00:00:00Z date_updated: 2025-12-01T15:08:54Z day: '25' ddc: - '500' department: - _id: JaMa doi: 10.1214/25-ECP717 ec_funded: 1 external_id: arxiv: - '2404.15205' isi: - '001611557000018' file: - access_level: open_access checksum: 67858edbd74658fe38955fa1216f2f18 content_type: application/pdf creator: dernst date_created: 2025-11-04T07:34:05Z date_updated: 2025-11-04T07:34:05Z file_id: '20596' file_name: 2025_ElectronJourProbab_Brigati.pdf file_size: 278078 relation: main_file success: 1 file_date_updated: 2025-11-04T07:34:05Z has_accepted_license: '1' intvolume: ' 30' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '09' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Electronic Communications in Probability publication_identifier: eissn: - 1083-589X publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' related_material: record: - id: '17353' relation: earlier_version status: public scopus_import: '1' status: public title: Heat flow, log-concavity, and Lipschitz transport maps tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2025' ... --- OA_place: publisher OA_type: gold _id: '18897' 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.' 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" alternative_title: - TMLR article_processing_charge: No arxiv: 1 author: - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 citation: ama: 'Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. In: Transactions on Machine Learning Research. ; 2024.' apa: Pedrotti, F., Maas, J., & Mondelli, M. (2024). Improved convergence of score-based diffusion models via prediction-correction. In Transactions on Machine Learning Research. chicago: Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” In Transactions on Machine Learning Research, 2024. ieee: F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based diffusion models via prediction-correction,” in Transactions on Machine Learning Research, 2024. ista: Pedrotti F, Maas J, Mondelli M. 2024. Improved convergence of score-based diffusion models via prediction-correction. Transactions on Machine Learning Research. , TMLR, . mla: Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” Transactions on Machine Learning Research, 2024. short: F. Pedrotti, J. Maas, M. Mondelli, in:, Transactions on Machine Learning Research, 2024. corr_author: '1' date_created: 2025-01-27T12:18:05Z date_published: 2024-06-01T00:00:00Z date_updated: 2025-04-15T08:31:35Z day: '01' ddc: - '000' department: - _id: JaMa - _id: MaMo external_id: arxiv: - '2305.14164' file: - access_level: open_access checksum: 76a1fd5afd8ee6f7ae0e5912d7dbf6b4 content_type: application/pdf creator: dernst date_created: 2025-01-27T12:19:44Z date_updated: 2025-01-27T12:19:44Z file_id: '18898' file_name: 2024_TMLR_Pedrotti.pdf file_size: 780315 relation: main_file success: 1 file_date_updated: 2025-01-27T12:19:44Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 059876FA-7A3F-11EA-A408-12923DDC885E name: Prix Lopez-Loretta 2019 - Marco Mondelli publication: Transactions on Machine Learning Research publication_identifier: issn: - 2835-8856 publication_status: published quality_controlled: '1' related_material: record: - id: '17350' relation: earlier_version status: public scopus_import: '1' status: public title: Improved convergence of score-based diffusion models via prediction-correction tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- OA_place: publisher _id: '17336' 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" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Pedrotti F. Functional inequalities and convergence of stochastic processes. 2024. doi:10.15479/at:ista:17336 apa: Pedrotti, F. (2024). Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17336 chicago: Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic Processes.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17336. ieee: F. Pedrotti, “Functional inequalities and convergence of stochastic processes,” Institute of Science and Technology Austria, 2024. ista: Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria. mla: Pedrotti, Francesco. Functional Inequalities and Convergence of Stochastic Processes. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17336. short: F. Pedrotti, Functional Inequalities and Convergence of Stochastic Processes, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-07-29T09:14:14Z date_published: 2024-07-31T00:00:00Z date_updated: 2026-04-07T13:00:03Z day: '31' ddc: - '500' - '510' - '515' - '519' degree_awarded: PhD department: - _id: GradSch - _id: JaMa doi: 10.15479/at:ista:17336 ec_funded: 1 file: - access_level: open_access checksum: 11650bab714ef85ad43a287060850523 content_type: application/pdf creator: fpedrott date_created: 2024-08-02T09:23:26Z date_updated: 2024-08-02T09:23:26Z file_id: '17366' file_name: thesis_final.pdf file_size: 2941599 relation: main_file success: 1 - access_level: closed checksum: c30ba5611941226cf1bfc867c25b1e80 content_type: application/x-zip-compressed creator: fpedrott date_created: 2024-08-02T09:27:15Z date_updated: 2024-08-02T09:27:15Z file_id: '17367' file_name: thesis_final_source.zip file_size: 6293375 relation: source_file file_date_updated: 2024-08-02T09:27:15Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '07' oa: 1 oa_version: Published Version page: '183' project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '17351' relation: part_of_dissertation status: public - id: '17353' relation: part_of_dissertation status: public - id: '17350' relation: part_of_dissertation status: public - id: '17352' relation: part_of_dissertation status: public - id: '17143' relation: part_of_dissertation status: public status: public supervisor: - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 title: Functional inequalities and convergence of stochastic processes tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- _id: '17143' 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." 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 article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Dello Schiavo L, Maas J, Pedrotti F. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 2024;377(6):3779-3804. doi:10.1090/tran/9156 apa: 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. American Mathematical Society. https://doi.org/10.1090/tran/9156 chicago: Dello Schiavo, Lorenzo, Jan Maas, and Francesco Pedrotti. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions of the American Mathematical Society. American Mathematical Society, 2024. https://doi.org/10.1090/tran/9156. ieee: L. Dello Schiavo, J. Maas, and F. Pedrotti, “Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces,” Transactions of the American Mathematical Society, vol. 377, no. 6. American Mathematical Society, pp. 3779–3804, 2024. 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. mla: Dello Schiavo, Lorenzo, et al. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions of the American Mathematical Society, vol. 377, no. 6, American Mathematical Society, 2024, pp. 3779–804, doi:10.1090/tran/9156. short: L. Dello Schiavo, J. Maas, F. Pedrotti, Transactions of the American Mathematical Society 377 (2024) 3779–3804. date_created: 2024-06-16T22:01:06Z date_published: 2024-06-01T00:00:00Z date_updated: 2026-04-07T13:00:02Z day: '01' department: - _id: JaMa doi: 10.1090/tran/9156 ec_funded: 1 external_id: arxiv: - '2304.05239' isi: - '001203273300001' intvolume: ' 377' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2304.05239 month: '06' oa: 1 oa_version: Preprint page: 3779-3804 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c grant_number: E208 name: Configuration Spaces over Non-Smooth Spaces publication: Transactions of the American Mathematical Society publication_identifier: eissn: - 1088-6850 issn: - 0002-9947 publication_status: published publisher: American Mathematical Society quality_controlled: '1' related_material: record: - id: '17336' relation: dissertation_contains status: public scopus_import: '1' status: public title: Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 377 year: '2024' ... --- OA_place: repository _id: '17350' 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." article_processing_charge: No arxiv: 1 author: - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 citation: ama: Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. arXiv. doi:10.48550/arXiv.2305.14164 apa: Pedrotti, F., Maas, J., & Mondelli, M. (n.d.). Improved convergence of score-based diffusion models via prediction-correction. arXiv. https://doi.org/10.48550/arXiv.2305.14164 chicago: Pedrotti, Francesco, Jan Maas, and Marco Mondelli. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2305.14164. ieee: F. Pedrotti, J. Maas, and M. Mondelli, “Improved convergence of score-based diffusion models via prediction-correction,” arXiv. . ista: Pedrotti F, Maas J, Mondelli M. Improved convergence of score-based diffusion models via prediction-correction. arXiv, 10.48550/arXiv.2305.14164. mla: Pedrotti, Francesco, et al. “Improved Convergence of Score-Based Diffusion Models via Prediction-Correction.” ArXiv, doi:10.48550/arXiv.2305.14164. short: F. Pedrotti, J. Maas, M. Mondelli, ArXiv (n.d.). corr_author: '1' date_created: 2024-07-31T07:56:40Z date_published: 2024-06-06T00:00:00Z date_updated: 2026-04-07T13:00:02Z day: '06' department: - _id: JaMa - _id: MaMo doi: 10.48550/arXiv.2305.14164 external_id: arxiv: - '2305.14164' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2305.14164 month: '06' oa: 1 oa_version: Preprint project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 059876FA-7A3F-11EA-A408-12923DDC885E name: Prix Lopez-Loretta 2019 - Marco Mondelli publication: arXiv publication_status: draft related_material: record: - id: '18897' relation: later_version status: public - id: '17336' relation: dissertation_contains status: public status: public title: Improved convergence of score-based diffusion models via prediction-correction type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- OA_place: repository _id: '17352' 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." article_number: '2402.04151' article_processing_charge: No arxiv: 1 author: - first_name: Kseniia full_name: Khudiakova, Kseniia id: 4E6DC800-AE37-11E9-AC72-31CAE5697425 last_name: Khudiakova orcid: 0000-0002-6246-1465 - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. arXiv. doi:10.48550/arXiv.2402.04151 apa: Khudiakova, K., Maas, J., & Pedrotti, F. (n.d.). L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model. arXiv. https://doi.org/10.48550/arXiv.2402.04151 chicago: Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” ArXiv, n.d. https://doi.org/10.48550/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,” arXiv. . 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. mla: Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” ArXiv, 2402.04151, doi:10.48550/arXiv.2402.04151. short: K. Khudiakova, J. Maas, F. Pedrotti, ArXiv (n.d.). corr_author: '1' date_created: 2024-07-31T08:07:40Z date_published: 2024-02-07T00:00:00Z date_updated: 2026-04-07T13:00:02Z day: '07' department: - _id: JaMa doi: 10.48550/arXiv.2402.04151 external_id: arxiv: - '2402.04151' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2402.04151 month: '02' oa: 1 oa_version: Preprint project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8 grant_number: '26293' name: The impact of deleterious mutations on small populations publication: arXiv publication_status: draft related_material: record: - id: '20050' relation: later_version status: public - id: '17336' relation: dissertation_contains status: public status: public title: L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- OA_place: repository _id: '17353' abstract: - lang: eng 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." article_number: '2404.15205' article_processing_charge: No arxiv: 1 author: - first_name: Giovanni full_name: Brigati, Giovanni id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1 last_name: Brigati - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. arXiv. doi:10.48550/arXiv.2404.15205 apa: Brigati, G., & Pedrotti, F. (n.d.). Heat flow, log-concavity, and Lipschitz transport maps. arXiv. https://doi.org/10.48550/arXiv.2404.15205 chicago: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2404.15205. ieee: G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport maps,” arXiv. . ista: Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. arXiv, 2404.15205. mla: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” ArXiv, 2404.15205, doi:10.48550/arXiv.2404.15205. short: G. Brigati, F. Pedrotti, ArXiv (n.d.). corr_author: '1' date_created: 2024-07-31T08:17:14Z date_published: 2024-05-08T00:00:00Z date_updated: 2026-04-07T13:00:02Z day: '08' department: - _id: JaMa doi: 10.48550/arXiv.2404.15205 external_id: arxiv: - '2404.15205' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2404.15205 month: '05' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '20591' relation: later_version status: public - id: '17336' relation: dissertation_contains status: public status: public title: Heat flow, log-concavity, and Lipschitz transport maps type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- OA_place: repository _id: '17351' 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." article_number: '2308.00516' article_processing_charge: No arxiv: 1 author: - first_name: Francesco full_name: Pedrotti, Francesco id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c last_name: Pedrotti citation: ama: Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. arXiv. doi:10.48550/arXiv.2308.00516 apa: Pedrotti, F. (n.d.). Contractive coupling rates and curvature lower bounds for Markov chains. arXiv. https://doi.org/10.48550/arXiv.2308.00516 chicago: Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2308.00516. ieee: F. Pedrotti, “Contractive coupling rates and curvature lower bounds for Markov chains,” arXiv. . ista: Pedrotti F. Contractive coupling rates and curvature lower bounds for Markov chains. arXiv, 2308.00516. mla: Pedrotti, Francesco. “Contractive Coupling Rates and Curvature Lower Bounds for Markov Chains.” ArXiv, 2308.00516, doi:10.48550/arXiv.2308.00516. short: F. Pedrotti, ArXiv (n.d.). corr_author: '1' date_created: 2024-07-31T08:02:16Z date_published: 2023-08-02T00:00:00Z date_updated: 2026-04-07T13:00:02Z day: '02' department: - _id: JaMa doi: 10.48550/arXiv.2308.00516 external_id: arxiv: - '2308.00516' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2308.00516 month: '08' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '20040' relation: later_version status: public - id: '17336' relation: dissertation_contains status: public status: public title: Contractive coupling rates and curvature lower bounds for Markov chains type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ...