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.
Operator limits of random matrices
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abstract
We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are discussed.
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cond-mat.stat-mech 1years
2025 1verdicts
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The Tracy-Widom distribution at large Dyson index
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.