Mean Field Systems on Random Graphs
发布时间:2022年06月20日
浏览次数:3393
发布者: He Liu
主讲人: Ruoyu Wu (Iowa State University)
活动时间: 从 2022-06-22 10:00 到 2022-07-01 11:30
场地: 线上
Weakly interacting particle systems and their mean field limits given by McKean—Vlasov processes have been extensively studied and arise in many areas, such as neuroscience, queueing theory, social sciences, etc. A typical feature of such systems is that the evolution of a particle’s state depends on the empirical distribution of all particles’ states. In recent years, there have been a growing interest in mean field systems on random graphs. Such systems consist of a large number of nodes in which the state of each node is governed by a stochastic process that has a mean-field type interaction with the neighboring nodes.
In this mini course, we will first review the classic mean field theory, including the propagation of chaos, law of large numbers, and central limit theorems. Then we will present how dense graphs, which could be random/deterministic/homogeneous/heterogeneous, affect the large population asymptotic behavior while sharing many similarities with the classic case. Finally we will present the significant impact of sparse graphs on the large population asymptotics of both a fixed particle and the empirical measure of the whole system.
Topics:
1. Mean field systems and propagation of chaos2. Dense random graphs and graphon mean field systems
3. Sparse random graphs, local weak convergence, and Markov random fields
Some reference:
[1] C. Bordenave. Lecture notes on random graphs and probabilistic combinatorial optimization. 2016.[2] L. Lovász. Large networks and graph limits (Vol. 60). American Mathematical Society, 2012.
[3] AS. Sznitman. Topics in propagation of chaos. Lecture Notes in Mathematics, vol 1464. Springer, Berlin, Heidelberg, 1991.
[4] R. van der Hofstad. Random graphs and complex networks, volumes 1 and 2.
Time:June 22, 24, 29, July 1, 10-11:30 am (Beijing Time)
点击链接入会,或添加至会议列表:
https://meeting.tencent.com/dm/xeHauGAPjoms
腾讯会议:989-9487-8560
https://meeting.tencent.com/dm/xeHauGAPjoms
腾讯会议:989-9487-8560