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Typical fluctuations ofE 21: We have already shown that, atβ≫1, pairs of eigenvalues follow a multivariate Gaussian distribution

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The Tracy-Widom distribution at large Dyson index

cond-mat.stat-mech · 2025-10-16 · conditional · novelty 7.0

For large beta the TW density takes the form exp(-beta Phi(a)) with Phi(a) obtained as the solution of a Painleve II equation via saddle-point analysis of the stochastic Airy operator.

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  • The Tracy-Widom distribution at large Dyson index cond-mat.stat-mech · 2025-10-16 · conditional · none · ref 1

    For large beta the TW density takes the form exp(-beta Phi(a)) with Phi(a) obtained as the solution of a Painleve II equation via saddle-point analysis of the stochastic Airy operator.