Student Probability Seminar

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Introduction to Directed Polymers

Speaker: Douglas Dow, CIMS

Location: Warren Weaver Hall 517

Date: Monday, November 15, 2021, 11:30 a.m.

Synopsis:

Abstract: In this introductory talk I will motivate the definition of a polymer measure as a (random) measure on paths that interpolates between that of a random walk and an action maximizing path. A directed polymer models a chain of particles lying in a random energy potential at a particular temperature. I will introduce the log partition function as a key object of interest and sketch of proof that it has an almost sure, non-random limit. Time permitting, I will discuss the concept of phase transition as the temperature increases, and how this pertains to localization of the polymer around favored regions.