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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Timo Seppalainen
University of Wisconsin
Title: Kardar-Parisi-Zhang universality and the exactly solvable log-gamma polymer

Abstract: The KPZ universality class consists of stochastic models of interacting particles, random paths in random media and growth models that share characteristics such as certain fluctuation exponents and limiting probability distributions that come from random matrix theory. The class is named after an influential 1986 physics paper by Kardar, Parisi and Zhang. Systems in the KPZ class do not manifest the familiar diffusive or Gaussian behavior captured by the classic central limit theorem. Investigations of the KPZ class have thus far relied on a handful of exactly solvable models whose special features permit detailed analysis. This talk is a colloquium-style introduction to the log-gamma polymer, an exactly solvable model in the category of random paths in random media. The features that make this model exactly solvable are a tractable translation-invariant version and connections with the combinatorics of the so-called geometric Robinson-Schensted-Knuth correspondence and special functions known as class one Whittaker functions. These properties enable rigorous proofs of fluctuation exponents, Tracy-Widom limit distributions, and some large deviation rate functions.

Recording: http://mm.math.cmu.edu/recordings/cna/timo_seppalainen_small.mp4
Date: Tuesday, November 24, 2015
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer