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.
Lei Ying received his B.E. degree from Tsinghua University, Beijing, China, and his M.S. and Ph.D. in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign. He currently is an Associate Professor at the School of Electrical, Computer and Energy Engineering at Arizona State University, and an Associate Editor of the IEEE/ACM Transactions on Networking. His research interest is broadly in the area of stochastic networks, including data privacy, social networks, cloud computing, and communication networks. He is coauthor with R. Srikant of the book Communication Networks: An Optimization, Control and Stochastic Networks Perspective, Cambridge University Press, 2014.
He won the Young Investigator Award from the Defense Threat Reduction Agency (DTRA) in 2009 and NSF CAREER Award in 2010. He was the Northrop Grumman Assistant Professor in the Department of Electrical and Computer Engineering at Iowa State University from 2010 to 2012. He received the best paper award at IEEE INFOCOM 2015.