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Precise asymptotics for random matrices and random growth models

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Abstract

The author considers the largest eigenvalues 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.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China

    Zhong Gen Su

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  1. Zhong Gen Su
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Correspondence to Zhong Gen Su.

Additional information

Supported partly by NSF of China (No. 10371109, 10671176) and the Royal Society K. C. Wong Education Foundation

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Su, Z.G. Precise asymptotics for random matrices and random growth models. Acta. Math. Sin.-English Ser. 24, 971–982 (2008). https://doi.org/10.1007/s10114-007-6365-8

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