@misc{10481/106052,
year = {2025},
url = {https://hdl.handle.net/10481/106052},
abstract = {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.},
organization = {European Union’s Horizon Europe - Marie Skłodowska-Curie (agreement no. 101064402, grant C-EXP265-UGR23)},
organization = {MICIU/AEI/10.13039/501100011033 - ERDF/EU  (PID2022-137228OB-I00)},
publisher = {Cornell University},
title = {Uniform contractivity of the Fisher infinitesimal model with strongly convex selection},
doi = {10.2140/apde.2025.18.1835},
author = {Calvez, Vicent and Martínez Poyatos, David Jesús and Santambrogio, Filippo},
}