Precise Asymptotics for Random Matrices and Random Growth Models  

作　　者：Zhong Gen SU 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第6期971-982,共12页数学学报（英文版）

基　　金：NSF of China (No.10371109,10671176);the Royal Society K.C.Wong Education Foundation

摘　　要：The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.

关 键 词：Gaussian unitary ensemble Laguerre unitary ensemble largest eigenvalues random growth models Tracy-Widom distribution 

分 类 号：O211[理学—概率论与数理统计]