Research

Research Interests

My main area of research is processes in random environments. Most of my research has been in random walks in random environments, but recently I have become interested in other processes (such as interacting particle systems) in random environments. I'm also interested in other non-classical random walks - especially the multi-excited random walk (also called the cookie random walk).

For a more complete description of my interests see my research statement .

Probability Seminar

This year I am organizing the Cornell Probability Theory Seminar.

Random Environments Conference

Together with Firas Rassoul-Agha, I am organizing a conference on random environments to be held May 1-3, 2011 at Cornell University.

Preprints and Publications

• Jon Peterson & Gennady Samorodnitsky, (2010) Weak quenched limiting distributions for transient one-dimensional random walk in a random environment. Submitted for publication.
• Jon Peterson, (2010) The contact process on the complete graph with random vertex-dependent infection rates . Stochastic Processes and their Applications. 121(3), pp. 609-629.
• Nina Gantert & Jon Peterson, (2009) Maximal displacement for bridges of random walks in a random environment . To appear in the Ann. Inst. H. Poincaré Probab. Statist.
• Jon Peterson & Timo Seppalainen, (2009) Current fluctuations of a system of one-dimensional random walks in random environment . Ann. Probab., 37, no. 1, pp. 143-188.
• Jon Peterson, (2010) Systems of one-dimensional random walks in a common random environment . Electronic Journal of Probability 15, pp. 1024-1040.
• Jon Peterson & Ofer Zeitouni, (2009) On the annealed large deviation rate function for a multi-dimensional random walk in random environment . ALEA Lat. Am. J. Probab. Math. Stat. , 6, pp. 349-368.
• Jon Peterson, (2008) Limiting distributions and large deviations for random walks in random environments . PhD Thesis - University of Minnesota.
• Jon Peterson, (2009) Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment . Ann. Inst. H. Poincaré Probab. Statist., 45, no. 3, pp. 685-709.
• Jon Peterson & Ofer Zeitouni, (2009) Quenched limits for transient, zero-speed one-dimensional random walk in random environment. Ann. Probab., 37, no. 1, pp. 143-188.

Presentations

• Quenched Limit Laws for Transient, One-Dimensional RWRE
• A Random Walk Through Electrical Engineering
• Properties of the Annealed Large Deviation Rate Function for a Random Walk in Random Environment
• Thesis Presentation
• RWRE Current Process
• Non-classical Random Walks
• Bridges of Random Walks in a Random Environment
• Linear Algebra and the Bowl Championship Series
• Weak Quenched Limiting Distributions for One-dimensional RWRE

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