RIGHT TAIL ASYMPTOTIC EXPANSION OF TRACY–WIDOM BETA LAWS

2011/11/11 by Gaëtan Borot, GAËTAN BOROT, Céline Nadal +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Asymptotic expansion #BETA (programming language) #Eigenvalues and eigenvectors #Function (biology) #Gaussian #Mathematical functions and polynomials #Matrix (chemical analysis) #Order (exchange) #Random Matrices and Applications #Scaling #Spectrum (functional analysis) #math-ph #math.MP #msc:30Exx #msc:60Bxx #msc:82Bxx

paper · pdf · doi:10.1142/s2010326312500062

published as Random Matrices: Theory and Applications (2012) · 23 pages

arxiv created 2011/11/11 · openalex publication_date 2012/07/01 · arxiv updated 2012/08/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian β matrix ensembles, to all orders in 1/N. We then give a physical derivation of the all order asymptotic expansion of the right tail of Tracy–Widom β laws, for all β > 0, by studying the double scaling limit.

Citations

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• On the Distribution of the Roots of Certain Symmetric Matrices