Mathematical Sciences: Limit and Averaging Theorems in Ergodic Theory

研究人员将在 遍历理论，它研究的平均，长期的行为， 逐步迭代或连续流动的变换。 他们的项目涉及到各种各样的主题： 分析，概率，谐波分析，组合学，和 数论 Sucheston教授将与线性变换 某些函数空间，也会追求多参数极限 向量值随机过程定理和预言者定理 在随机决策理论中。 除了古典 遍历理论中的收敛问题，Rosenblatt教授 将调查的唯一性和存在不变的手段， 群体行动和群体上的随机游走 他对群体的研究 将由博士后杨博士补充， 参与这个项目。 伯格森教授会集中精力 关于动力系统中的多重递归和混合， 数论和组合数学的应用。 总 预计这一努力将受益于四国之间的合作 研究人员

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.