Mean Field Analysis: Applications, Convergence, and the Rate of Convergence


Lei Ying
Arizona State University

Wednesday, April 13, 2016
4:15 - 5:15 PM
Location: Huang 305


Abstract:

Abstract: Mean-field analysis is a method to study large-scale and complex stochastic systems. The idea is to assume the states of nodes in a large-scale system are independently and identically distributed (i.i.d.). Based on this i.i.d. assumption, in a large-scale system, the interaction of a node to the rest of the system can be replaced with an “average” interaction, and the evolution of the system can then be modeled as a deterministic dynamical system, called a mean-field model. Then the macroscopic behaviors of the stochastic system can be approximated using the solution of the mean-field model, in particular, the stationary distribution of the stochastic system can be approximated using the equilibrium point of the mean-field model. This talk will first review a few applications of mean-field analysis and existing methods to prove the convergence of stationary distributions of stochastic systems to the equilibrium point of the mean-field model. Then, I will present a new method to prove not only the convergence but also the rate of convergence to the mean-field limit. The method identifies a fundamental connection between the perturbation theory for nonlinear systems and the convergence of mean-field models via Stein’s method. This result quantifies the approximation error of using the mean-field solution for a finite-size stochastic system, which cannot be obtained under the existing methods that prove the convergence based on the interchange of the limits.

---

Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html