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

该奖项将支持助理教员Steven Kalikow的工作。建议的工作是概率和遍历理论的混合。遍历的理论主题寻求一种表达转换的方法，一种构造新转换的方法，以及关于混合是否意味着三重混合这一问题的新方法。概率主题涉及平稳度量的度量、相变和寻找两个随机变量序列的最长公共子序列。这项工作处于这两个学科的交界处。这项工作的一个应用是在DNA序列比对领域，即个人正在寻找两个DNA序列的公共子序列。

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.