Weakly interacting particle systems on inhomogeneous random graphs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Bhamidi, Shankar¹  Budhiraja, Amarjit¹  Wu, Ruoyu² 

[1] Univ N Carolina, Dept Stat & Operat Res, 304 Hanes Hall, Chapel Hill, NC 27599 USA

[2] Brown Univ, Div Appl Math, 182 George St, Providence, RI 02912 USA

关键词: Inhomogeneous random graphs;    Dynamical random graphs;    Weakly interacting diffusions;    Propagation of chaos;    Central limit theorems;    Multi-type populations;    Interacting particle systems;   

DOI  :  10.1016/j.spa.2018.06.014

来源: Elsevier

【 摘 要 】

We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The collection of neighbors of a given node changes dynamically over time and is determined through a time evolving random graph process. A law of large numbers and a propagation of chaos result is established for a multi-type population setting where at each instant the interaction between nodes is given by an inhomogeneous random graph which may change over time. This result covers the setting in which the edge probabilities between any two nodes are allowed to decay to 0 as the size of the system grows. A central limit theorem is established for the single-type population case under stronger conditions on the edge probability function. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free