Mathematical Sciences: Limit and Averaging Theorems in Ergodic Theory

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The investigators will conduct mathematical research in ergodic theory, which studies the average, long-run behavior of stepwise iterated or continuously flowing transformations. Their project impinges upon a variety of subjects: functional analysis, probability, harmonic analysis, combinatorics, and number theory. Professor Sucheston will work with linear transformations of certain function spaces and will also pursue multiparameter limit theorems for vector-valued random processes, and prophet theorems in stochastic decision theory. In addition to classical questions of convergence in ergodic theory, Professor Rosenblatt will investigate uniqueness and existence of invariant means for group actions, and random walks on groups. His work on groups will be complemented by that of Dr. Yang, a postdoctoral associate on this project. Professor Bergelson will concentrate on multiple recurrence and mixing in dynamical systems, with applications to number theory and combinatorics. The total effort is expected to benefit from cooperation among the four researchers.