Title: Large-graph approximations for stochastic processes on (random) graphs and their applications
Abstract: In this talk, we focus on stochastic processes on (random) graphs. They arise naturally in epidemiology, statistical physics, computer science and engineering disciplines. In this set-up, the vertices are endowed with a local state (e.g., immunological status in case of an epidemic process, opinion about a social situation, buffer availability in case of a video streaming system, queue length in models of queueing theory). The local state changes dynamically as the vertex interacts with its neighbours. The interaction rules and the graph structure depend on the application-specific context. We will discuss (non-equilibrium) approximation methods for those systems as the number of vertices grow large.
In particular, we will discuss three different approximations in this talk: i) approximate lumpability of Markov processes based on local symmetries (local automorphisms) of the graph, ii) functional laws of large numbers in the form of ordinary and partial differential equations, and iii) functional central limit theorems in the form of Gaussian semi-martingales. We will also briefly discuss how those approximations lead to “nice” random measures that could be used for practical purposes, such as parameter inference from real epidemic data (e.g. COVID-19 in Ohio), designing “optimal” policies etc.
Zoom information: To join the seminar by zoom, please use the following link:
https://osu.zoom.us/j/93066786961?pwd=aGxpQitJUmNLNlRqSi9naXBmWWx4dz09
Video: https://osu.box.com/s/jme1t6duhshft6hpqg2q1v14b0rv2js7