Mathematical Sciences: Limit and Averaging Theorems in Ergodic Theory

研究人员将在遍历理论中进行数学研究，该理论研究逐步迭代或连续流动变换的平均、长期行为。他们的项目涉及到各种学科：泛函分析、概率、调和分析、组合学和数论。Sucheston教授将致力于某些函数空间的线性变换，还将研究向量值随机过程的多参数极限定理，以及随机决策理论中的预言性定理。除了遍历理论中的经典收敛问题外，Rosenblatt教授还将研究群行动和群上随机游动的不变平均的唯一性和存在性。他在小组方面的工作将得到该项目的博士后助理杨博士的补充。伯格尔森教授将专注于动力系统中的多重递归和混合，以及在数论和组合学中的应用。预计这项总努力将受益于四名研究人员之间的合作。

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.