Mathematical Sciences: Form of Stationary Process, Common Subsequences and Phase Transition

该奖项将支持教师助理Steven Kalikow的工作。所提出的工作是概率论和遍历论的混合。遍历理论主题寻求一种表达转换的方式，一种构建新转换的方式，以及解决混合是否意味着三重混合问题的新方法。概率主题包括对平稳测度的度量，相变，以及寻找两个随机变量序列的最长公共子序列。这项工作是这两个学科的交汇处。这项工作的一个应用是在DNA序列比对领域，其中个人正在寻找两个DNA序列的共同子序列。

This award will support the work of faculty associate Steven Kalikow. The proposed work is a mixture of probability and ergodic theory. The ergodic theory topics seek a way of expressing transformations, a way of constructing new transformations, and new approaches to the question of whether mixing implies threefold mixing. The probability topics involve a measure on stationary measures, phase transition, and finding the longest common subsequence of two sequences of random variables. The work is at the interface of these two disciplines. One application of the work is in the area of DNA sequence alignment, where individuals are looking for common subsequences of two DNA sequences.