Mathematical Sciences: Stochastic Matrix Analysis

主要研究涉及马尔可夫链、随机矩阵及其应用的理论和计算问题。他研究了随机矩阵的Perron特征向量的敏感性，开发了计算该特征向量的有效方法，并研究了随机矩阵的结构及其相关的马尔可夫链。计算方法包括适用于并行处理器的算法。随机矩阵和马尔可夫链自然出现在工程、经济学、运筹学、物理和社会科学等广泛领域的问题表述中——例如，在计量经济学模型和客户随机到达的调度问题中。当以方程组的形式来描述时，许多这样的问题都具有与系统的特征向量相对应的特征。

The principal investigator studies theoretical and computational problems involving Markov chains, stochastic matrices, and their applications. He examines the sensitivity of the Perron eigenvector of a stochastic matrix, develops efficient methods to compute that eigenvector, and studies the structure of stochastic matrices and their related Markov chains. Computational methods include algorithms suitable for parallel processors. Stochastic matrices and Markov chains arise naturally in the formulation of problems in a broad variety of areas in engineering, economics, operations research, and the physical and social sciences -- for example, in econometric models and in scheduling problems where the clients to be served arrive in random fashion. When cast in the form of a system of equations, many such problems have features that correspond to the eigenvectors of the system.