Student Probability Seminar

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Localization of Directed Polymers

Speaker: Douglas Dow, CIMS

Location: Warren Weaver Hall 517

Date: Tuesday, September 27, 2022, 1 p.m.

Synopsis:

Often models of physical systems involve on the one hand an energy which the systems seeks to minimize and on the other hand noisy thermal fluctuations that frustrates the descent to a ground state. One can ask the extent to which energy dominates versus randomness by asking whether the system localizes around ground states with high probability. In this talk I will introduce the directed polymer model, a model involving a random walk interacting with a random environment, and I will discuss the concept of localization of the polymer measure. One surprising fact is that this Gibbs reweighting of a random walk is sufficient to counteract the diffusive effects of a random walk and to force the resulting measure on paths to concentrate in constant order regions.