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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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Speed of random walks in groups

For nilpotent groups the speed exponent is 0.5. See this paper for the general picture http://arxiv.org/abs/1203.6226 .
Dan Sălăjan's user avatar