Scaling limits for a population model with growth, division and cross-diffusion
Analysis of PDEs
2025-01-07 v2 Probability
Abstract
Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic stochastic model, write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. Under smoothness and symmetry assumptions for the interaction kernel, we then obtain entropy estimates, which provide us with a localization limit at the macroscopic level. Finally, we perform a thorough numerical study in order to compare the three modeling scales.
Cite
@article{arxiv.2410.13329,
title = {Scaling limits for a population model with growth, division and cross-diffusion},
author = {Marie Doumic and Sophie Hecht and Marc Hoffmann and Diane Peurichard},
journal= {arXiv preprint arXiv:2410.13329},
year = {2025}
}