{"publication":"The Annals of Applied Probability","corr_author":"1","date_updated":"2025-08-04T08:59:10Z","date_created":"2025-07-21T08:13:54Z","day":"01","issue":"3","type":"journal_article","date_published":"2025-06-01T00:00:00Z","publication_identifier":{"issn":["1050-5164"]},"page":"1913-1940","publisher":"Institute of Mathematical Statistics","title":"L∞-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal model","publication_status":"published","oa_version":"Preprint","scopus_import":"1","quality_controlled":"1","_id":"20050","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.","arxiv":1,"year":"2025","month":"06","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293","name":"The impact of deleterious mutations on small populations"}],"abstract":[{"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.","lang":"eng"}],"status":"public","doi":"10.1214/25-aap2162","intvolume":"        35","article_type":"original","volume":35,"department":[{"_id":"JaMa"}],"external_id":{"arxiv":["2402.04151"]},"author":[{"id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","first_name":"Kseniia","last_name":"Khudiakova","orcid":"0000-0002-6246-1465","full_name":"Khudiakova, Kseniia"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","last_name":"Maas","full_name":"Maas, Jan","first_name":"Jan"},{"full_name":"Pedrotti, Francesco","last_name":"Pedrotti","first_name":"Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c"}],"citation":{"short":"K. Khudiakova, J. Maas, F. Pedrotti, The Annals of Applied Probability 35 (2025) 1913–1940.","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>.","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>","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>.","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.","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."},"OA_type":"green","oa":1,"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2402.04151"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"17352"}]}}