# Probability Seminar

From UW-Math Wiki

## Fall 2010

Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. If you would like to receive announcements about upcoming seminars, please visit this page to sign up for the email list.

## Friday, September 3, 4PM B239 Timo Seppäläinen (UW Madison) (Math Colloquium)

- Title:
**Scaling exponents for a 1+1 dimensional directed polymer**

- Abstract: Directed polymer in a random environment is a model from statistical physics that has been around for 25 years. It is a type of random walk that evolves in a random potential. This means that the walk lives in a random landscape, some parts of which are favorable and other parts unfavorable to the walk. The objective is to understand the behavior of the walk on large space and time scales.
- I will begin the talk with simple random walk straight from undergraduate probability and explain what diffusive behavior of random walk means and how Brownian motion figures into the picture. The recent result of the talk concerns a particular 1+1 dimensional polymer model: the order of magnitude of the fluctuations of the polymer path is described by the exponent 2/3, in contrast with the exponent 1/2 of diffusive paths. Finding a rigorous proof of this exponent has been an open problem since the introduction of the model.

## Thursday, September 16, Gregorio Moreno Flores (UW - Madison)

- Title:
**Asymmetric directed polymers in random environments.**

- Abstract: It is well known that the asymetric last passage percolation problem can be approximated by a Brownian percolation model, wich is itself related to the GUE random matrices. This allows to transfer many results about random matrices to the setting of asymetric last passage percolation.
- In this talk, we will introduce two different schemes to treat asymmetric directed polymers in random environments.

## Thursday, September 30, Brian Rider (University of Colorado at Boulder)

- Title:
**TBA**

## Thursday, October 14, MIDWEST PROBABILITY COLLOQUIUM, (no seminar)

## Thursday, October 21, Michael Cranston (University of California, Irvine)

- Title:
**TBA**

## Thursday, October 28, Tom Alberts (University of Toronto)

- Title:
**TBA**