Mathematical Sciences: Research in Probability With Applications to Statistical Mechanics & Queueing Networks

首席研究员将在该地区进行研究 大的偏差。 特别是，他将开展项目， 三个主题：（a）马尔可夫链的大偏差 抽象空间中的值;（B）大偏差，极限 定理和统计力学中的相变;（c） 不连续马氏过程的大偏差 统计”和应用到网络的应用。 大偏差理论是概率论的一个分支 涉及随机变量的极限 众所周知在 某些理想化的情况下，其中随机变量是 独立和同分布，平均值 序列收敛于单个随机序列的平均值 变量（就统计学而言，样本平均值 平均值）。 大偏差理论 表明样本平均值偏离 以少量平均总体是指数小的 随着样本量的增加。 主要研究者 在更困难的情况下， 变量，其依赖结构遵循马尔可夫过程。 这一理论在统计学上有许多应用 力学和网络。

The principal investigator will conduct research in the area of large deviations. In particular, he will conduct projects on three topics: (a) large deviations for Markov chains taking values in an abstract space; (b) large deviations, limit theorems, and phase transitions in statistical mechanics; (c) large deviations for Markov processes with "discontinuous statistics" and applications to queueing networks. Large deviation theory is a branch of probability theory involving limits of random variables. It is well known that in certain idealized cases, where the random variables are independent and identically distributed, that the average of the sequence converges to the average of the individual random variable (in terms of statistics, that the sample average converges to the population average). Large deviation theory shows that the probability that the sample average deviates from the population average by a small amount is exponentially small as the sample size increases. The principal investigator is working in the much more difficult case of dependent random variables, whose dependence structure follows a Markov process. There are many applications of this theory to statistical mechanics and queueing networks.