 Quenched asymptotics for interacting diffusions on inhomogeneous random graphsEric Luçon Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 6783-6842 Abstract: 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 Erdős–Rényi 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. Keywords: Mean-field systems; Interacting diffusions; Spatially-extended systems; Neural field equation; Random graphs; Graph convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:11:p:6783-6842 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2020.06.010 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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