Uniform contractivity of the Fisher infinitesimal model with strongly convex selection Calvez, Vicent Martínez Poyatos, David Jesús Santambrogio, Filippo The Fisher infinitesimal model is a classical model of phenotypic trait inheritance in quantitative genetics. Here, we prove that it encompasses a remarkable convexity structure which is compatible with a selection function having a convex shape. It yields uniform contractivity along the flow, as measured by a version of the Fisher information. It induces in turn asynchronous exponential growth of solutions, associated with a well-defined, log-concave, equilibrium distribution. Although the equation is non-linear and non-conservative, our result shares some similarities with the Bakry-Emery approach to the exponential convergence of solutions to the Fokker-Planck equation with a convex potential. Indeed, the contraction takes place at the level of the Fisher information. Moreover, the key lemma for proving contraction involves the Wasserstein distance between two probability distributions of a (dual) backward-in-time process, and it is inspired by a maximum principle by Caffarelli for the Monge-Ampère equation. 2025-09-04T09:03:57Z 2025-09-04T09:03:57Z 2025 journal article Calvez, V., Poyato, D., & Santambrogio, F. (2025). Uniform contractivity of the Fisher infinitesimal model with strongly convex selection. In arXiv [math.PR]. https://doi.org/10.2140/apde.2025.18.1835 https://hdl.handle.net/10481/106052 10.2140/apde.2025.18.1835 eng info:eu-repo/grantAgreement/EC/H2020/MSC/101064402 http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Cornell University