Random Matrices and Applications

摘要大随机矩阵的特征值在数学、统计学和物理学中用于描述各种对象的极限行为，如随机排列、黎曼- ζ函数的零点、样本协方差矩阵、非相交路径和随机增长模型等。研究者计划研究随机矩阵理论中极限分布函数的各种内在性质，并将随机矩阵理论的思想和方法应用于最后通道渗透、排队模型、非相交路径和相互作用粒子系统等概率模型。建立在研究者和其他研究者早期工作的基础上，长期目标是利用可积系统和概率的思想，阐明用随机矩阵的特征值来描述的模型的通用性。

AbstractBaikThe eigenvalues of large random matrices are known to describe thelimiting behaviors of various objects in mathematics, statisticsand physics such as random permutations, zeros of Riemann-zetafunction, sample covariance matrices, non-intersecting paths andrandom growth models. The investigator plans to study variousintrinsic properties the limiting distribution functions arisingin random matrix theory, as well as to apply the ideas and methodsof random matrix theory to probability models such as last passagepercolation, queueing models, non-intersecting paths andinteracting particle systems. Built on the investigator's andother researchers' earlier work, the long term goal is to clarifythe universality class of models which are describable in terms ofthe eigenvalues of random matrices using ideas from bothintegrable systems and probability.