Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GOE
arXiv:0801.2620 · doi:10.1063/1.3046561
Abstract
In this paper we focus on the large n probability distribution function of the largest eigenvalue in the Gaussian Orthogonal Ensemble of n by n matrices (GOEn). We prove an Edgeworth type Theorem for the largest eigenvalue probability distribution function of GOEn. The correction terms to the limiting probability distribution are expressed in terms of the same Painleve II functions appearing in the Tracy-Widom distribution. We conclude with a brief discussion of the GSEn case.
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- Fast approach to the Tracy-Widom law at the edge of GOE and GUE
- A Stirling-type formula for the distribution of the length of longest increasing subsequences
- Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices
- Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited
- Asymptotic expansions relating to the distribution of the length of longest increasing subsequences