Transport maps for Beta-matrix models and Universality

2013/11/10 by Florent Bekerman, Alessio Figalli, Bekerman, Florent +3 · 1 citation
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1311.2315

openalex publication_date 2013/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct approximate transport maps for non-critical Beta-matrix models, that is, maps so that the push forward of a non-critical Beta-matrix model with a given potential is a non-critical Beta-matrix model with another potential, up to a small error in the total variation distance. As a consequence, we deduce that local statistics have the same asymptotic behavior for both models.

Citations

• Fluctuations of eigenvalues of matrix models and their applications

Cited by

• Anomalous energy correlations and spectral form factor in the nonergodic phase of the β-ensemble

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