Understanding rare events in models of statistical mechanics

Seminar | January 22 | 4:10-5 p.m. | 1011 Evans Hall

 Shirshendu Ganguly, UC Berkeley

 Department of Statistics

Statistical mechanics models are ubiquitous at the interface of probability theory, information
theory, and inference problems in high dimensions. In this talk, we will focus on
sparse networks, and polymer models on lattices. The study of rare behavior (large deviations)
is intimately related to the understanding of such models. In particular, we will
consider the rare events that a sparse random network has an atypical number of certain
local structures and that a polymer in random media has atypical weight. Such events can
have different geometric consequences, ranging from local to more global. We will discuss
some recent results concerning such phenomena, and connections to stochastic block models,
exponential random graphs, eigenvalues of random matrices, and fundamental growth