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Random walks in Random Environments
At each site x of Zd, put a (random) probability measure ωx on {-d,...,-1,1,...,d}, and then start a random walk that, when at site x, jumps to site x+e with probability ωx (e) for |e|=1. This model of a random walk in a random environment (RWRE) is arguably the simplest model of motion in random media one can think of. Many surprising properties of the RWRE have been discovered. For example, in dimension 1, the RWRE can exhibit sub-diffusive behavior, transience with zero average speed, and aging. Many challenges remain (for example, no criterion for transience or recurrence is known for d > 2. I will report on recent progress in the study of RWRE and on some surprising counter-examples to natural conjectures.
Thursday, March 4, 2004, 245 Altgeld Hall, 4:00 p.m.
Mathematics Colloquia homepage