The smallest eigenvalue distribution of the Jacobi unitary ensembles

DOI10.1002/MMA.7394zbMATH Open1472.60011arXiv2003.04911OpenAlexW3010723806MaRDI QIDQ4959178

Yang Chen, Shu-Lin Lyu

Publication date: 10 September 2021

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Abstract: In the hard edge scaling limit of the Jacobi unitary ensemble generated by the weight $$, the probability that all eigenvalues of Hermitian matrices from this ensemble lie in the interval $[t,1]$ is given by the Fredholm determinant of the Bessel kernel. We derive the constant in the asymptotics of this Bessel-kernel determinant. A specialization of the results gives the constant in the asymptotics of the probability that the interval $(-a,a),a>0,$ is free of eigenvalues in the Jacobi unitary ensemble with the symmetric weight $$.

Full work available at URL: https://arxiv.org/abs/2003.04911

zbMATH Keywords

Bessel kernelasymptotic expansionsFredholm determinantsmallest eigenvalue distributionJacobi unitary ensemble

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (2)

Smallest eigenvalue distribution of the fixed-trace Laguerre beta-ensemble ⋮ Cubature rules for unitary Jacobi ensembles

This page was built for publication: The smallest eigenvalue distribution of the Jacobi unitary ensembles

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4959178)