Program
 Tsinghua University Pao-Lu Hsu Distinguished Lecture Student No.： 100 Time： 【Updated】16:30-17:30, 2015-5-8/12 Instructor： David Aldous  [University of California, Berkeley] Place： Lecture hall, Floor 3, Jin Chun Yuan West Building Starting Date： 2015-5-8 Ending Date： 2015-5-12

Lecture 1: Interacting particle systems as stochastic social dynamics

Abstract: The style of mathematical models known to probabilists as Interacting Particle Systems and exemplified by the Voter, Exclusion and Contact processes have found use in many academic disciplines. Often the underlying conceptual picture is of a social network, where individuals meet pairwise and update their "state" (opinion, activity etc) in a way depending on the two previous states. This picture motivates a precise general setup we call Finite Markov Information Exchange (FMIE) processes. The talk will briefly describe a few less familiar models (Averaging, Deference, Fashionista) suggested by the social network picture, as well as some more familiar ones.

Lecture 2: The Compulsive Gambler and the Metric Coalescent

Abstract: In the Compulsive Gambler process there are n agents who meet pairwise at random times (i and j meet at times of a rate-\nu_{ij} Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the other's money. The process seems pedagogically interesting as being intermediate between coalescent-tree models and interacting particle models, and because of the variety of techniques available for its study. Some techniques are rather obvious (martingale structure; comparison with Kingman coalescent) while others are more subtle (an exchangeable over the money elements" property, and a token process" construction reminiscent of the Donnelly-Kurtz look-down construction). Also one can study both kinds of n \to \infty limit. The process can be defined under weak assumptions on a countable discrete space (nearest-neighbor interaction on trees, or long-range interaction on the d-dimensional lattice) and there is also a continuous-space extension called the Metric Coalescent, studied by my student Daniel Lanoue.

Introduction of Speaker:

David Aldous is Professor in the Statistics Dept at U.C. Berkeley, since 1979. He received his Ph.D. from Cambridge University in 1977. He is the author of "Probability Approximations via the Poisson Clumping Heuristic" and (with Jim Fill) of a notorious unfinished online work "Reversible Markov Chains and Random Walks on Graphs". His research in mathematical probability has covered weak convergence, exchangeability, Markov chain mixing times, continuum random trees, stochastic coalescence and spatial random networks. A central theme has been the study of large finite random structures, obtaining asymptotic behavior as the size tends to infinity via consideration of some suitable infinite random structure. He has recently become interested in articulating critically what mathematical probability says about the real world.

He is a Fellow of the Royal Society (U.K.), and a foreign associate of the National Academy of Sciences (USA).