Jonathon Peterson

Visiting Assistant Professor of Mathematics

Web Site Contact Information Office:  591 Malott Hall Phone:  (607) 255-8268 Fax:  (607) 255-7149 Email:  peterson@math.cornell.edu Courses & Office Hours

Education

Ph.D. (2008) University of Minnesota

Research Area: Discrete probability. Random walks in random environments.

My research area is probability theory. I am mostly interested in problems of discrete probability, particularly in random walks in random environments (RWRE). A random walk in a random environment is a simple model for random motion where the probability of moving from one site to another is location dependent and random.

Much of my research has been in one-dimensional RWRE. The one-dimensional model has the advantage that the random walk is reversible (given the environment), and thus explicit formulas for certain probabilities or expected values are easily obtained. These formulas allow for a very detailed (if sometimes cumbersome) analysis of the behavior of the random walk. Multi-dimensional RWRE are much more difficult in many ways. While much progress has been made in the last 10 years, there are still many unanswered questions (even to some of the most basic questions of recurrence/transience and laws of large numbers).

My most recent research has been in systems of (infinitely) many random walks evolving in the same random environment. Thus far I have worked only with systems of random walks that do not interact, but I hope to eventually analyze some of the common models of interacting particle systems evolving in a common random environment.

Selected Publications

Quenched limits for transient, zero-speed one-dimensional random walk in random environment (with Ofer Zeitouni), Ann. Probab. 37 no. 1 (2009), 143–188.

Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment, Ann. Inst. H. Poincaré Probab. Statist (to appear).

On the annealed large deviation rate function for a multi-dimensional random walk in random environment (with Ofer Zeitouni), arXiv:0812.3619 [math.PR].

Current fluctuations of a system of one-dimensional random walks in random environment (with Timo Seppäläinen). arXiv:0904.4768 [math.PR].

Last modified: September 11, 2009