Explicit asymptotic expansions in powers of h ~ n^{-2/3} are derived for the Tracy-Widom distributions F_beta describing the rescaled largest eigenvalues of Gaussian and Laguerre ensembles, with polynomial coefficients in derivatives of F_beta.
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Correction terms in soft-edge asymptotics for gap probabilities are multilinear forms in higher derivatives of the leading term, with rational polynomial coefficients independent of the generating variable.
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Asymptotic Expansions of the Limit Laws of Gaussian and Laguerre (Wishart) Ensembles at the Soft Edge
Explicit asymptotic expansions in powers of h ~ n^{-2/3} are derived for the Tracy-Widom distributions F_beta describing the rescaled largest eigenvalues of Gaussian and Laguerre ensembles, with polynomial coefficients in derivatives of F_beta.
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Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge III: Generating Functions
Correction terms in soft-edge asymptotics for gap probabilities are multilinear forms in higher derivatives of the leading term, with rational polynomial coefficients independent of the generating variable.