2022/07/22 by Alain Blaustein, Blaustein, Alain, Émeric Bouin +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum many-body systems #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2207.11010
openalex publication_date 2022/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we focus on a spatially extended FitzHugh-Nagumo model with interactions. In the regime where strong and local interactions dominate, we quantify how the probability density of neurons concentrates into a Dirac distribution. Previous work investigating this question have provided relative bounds in integrability spaces. Using a Hopf-Cole framework, we derive precise L^∞ estimates using subtle explicit sub- and super- solutions which prove, with rates of convergence, that the blow up profile is Gaussian.