Quenched asymptotics for interacting diffusions on inhomogeneous random graphs.
Quenched asymptotics for interacting diffusions on inhomogeneous random graphs.
复制标题
非齐次随机图上相互作用扩散的淬灭渐近。
DOI：
10.1016/j.spa.2020.06.010
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
E. Luçon
中科院分区：
文献类型：
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作者：
E. Luçon
本文的目的是解决在随机、可能稀释且不均匀的图表上相互作用的大量扩散的行为。这是先前工作的自然延续，其中考虑了同质的 Erdős-Rényi 案例。我们考虑的图类包括无序 W 随机图，以及可能无界的图元。主要结果涉及系统的经验测量的淬灭收敛（对于随机图的几乎所有实现都是如此），以解决具有空间扩展的非线性福克-普朗克偏微分方程，也出现在不同的环境中，特别是在神经科学中。还考虑了与扩散相关的空间分布的收敛性，并且证明了极限是用非线性积分微分方程描述的，该方程在某些特定情况下与神经场方程相匹配。
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.
影响因子：
1.1
作者：
Chiba, Hayato;Medvedev, Georgi S.
通讯作者：
Medvedev, Georgi S.
非Lipschitz极限图序列上Kuramoto模型的平均场方程
影响因子：
2
作者：
Kaliuzhnyi-Verbovetskyi, Dmitry;Medvedev, Georgi S.
通讯作者：
Medvedev, Georgi S.