Quenched asymptotics for interacting diffusions on inhomogeneous random graphs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Lucon, Eric¹ 

[1] Univ Paris, MAP5, UMR CNRS 8145, F-75006 Paris, France

关键词: Mean-field systems;    Interacting diffusions;    Spatially-extended systems;    Neural field equation;    Random graphs;    Graph convergence;   

DOI  :  10.1016/j.spa.2020.06.010

来源: Elsevier

【 摘 要 】

The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erdos-Renyi case was considered. The class of graphs we consider includes disordered W-random graphs, with possibly unbounded graphons. The main result concerns a quenched convergence (that is true for almost every realization of the random graph) of the empirical measure of the system towards the solution of a nonlinear Fokker-Planck PDE with spatial extension, also appearing in different contexts, especially in neuroscience. The convergence of the spatial profile associated to the diffusions is also considered, and one proves that the limit is described in terms of a nonlinear integro-differential equation which matches the neural field equation in certain particular cases. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free