# Graduate student reading seminar

Tuesdays at 2:30pm, VV B305 for the rest of the semester

## Contents

## 2014 Fall

9/23, 9/30

10/7, 10/14

10/21, 10/28

11/4, 11/11

11/18, 11/25

12/2, 12/9

## 2014 Spring

1/28: Greg

2/04, 2/11: Scott

Reflected Brownian motion, Occupation time, and applications.

2/18: Phil-- Examples of structure results in probability theory.

2/25, 3/4: Beth-- Derivative estimation for discrete time Markov chains

3/11, 3/25: Chris J Some classical results on stationary distributions of Markov processes

4/1, 4/8: Chris N

4/15, 4/22: Yu Sun

4/29. 5/6: Diane

## 2013 Fall

9/24, 10/1: Chris A light introduction to metastability

10/8, Dae Han Majoring multiplicative cascades for directed polymers in random media

10/15, 10/22: no reading seminar

10/29, 11/5: Elnur Limit fluctuations of last passage times

11/12: Yun Helffer-Sj?ostrand representation and Brascamp-Lieb inequality for stochastic interface models

11/19, 11/26: Yu Sun

12/3, 12/10: Jason

## 2013 Spring

2/13: Elnur

Young diagrams, RSK correspondence, corner growth models, distribution of last passage times.

2/20: Elnur

2/27: Chris

A brief introduction to enlargement of filtration and the Dufresne identity Notes

3/6: Chris

3/13: Dae Han

An introduction to random polymers

3/20: Dae Han

Directed polymers in a random environment: path localization and strong disorder

4/3: Diane

Scale and Speed for honest 1 dimensional diffusions

References:

Rogers & Williams - Diffusions, Markov Processes and Martingales

Ito & McKean - Diffusion Processes and their Sample Paths

Breiman - Probability

http://www.statslab.cam.ac.uk/~beresty/Articles/diffusions.pdf

4/10: Diane

4/17: Yun

Introduction to stochastic interface models

4/24: Yun

Dynamics and Gaussian equilibrium sytems

5/1: This reading seminar will be shifted because of a probability seminar.

5/8: Greg, Maso

The Bethe ansatz vs. The Replica Trick. This lecture is an overview of the two approaches. See [1] for a nice overview.

5/15: Greg, Maso

Rigorous use of the replica trick.