RIGHT TAIL ASYMPTOTIC EXPANSION OF TRACY–WIDOM BETA LAWS

DOI10.1142/S2010326312500062zbMath1266.60047arXiv1111.2761MaRDI QIDQ2920377

Celine Nadal, Gaëtan Borot

Publication date: 16 October 2012

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.2761

zbMATH Keywords

Large deviationsRandom MatricesTracy-Widom lawsGaussian Ensembles

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Extreme value theory; extremal stochastic processes (60G70) Large deviations (60F10)

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Cites Work

• Unnamed Item
• On the distribution of the roots of certain symmetric matrices
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• Asymptotics of the Airy-kernel determinant
• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Monodromy- and spectrum-preserving deformations. I
• Level-spacing distributions and the Airy kernel
• Universality at the edge of the spectrum in Wigner random matrices.
• On orthogonal and symplectic matrix ensembles
• Random matrices: Universality of local eigenvalue statistics up to the edge
• On fluctuations of eigenvalues of random Hermitian matrices.
• Sur la distribution limite du terme maximum d'une série aléatoire
• A pedestrian's view on interacting particle systems, KPZ universality and random matrices
• Statistical Theory of the Energy Levels of Complex Systems. I
• Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices
• Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem
• Matrix models for beta ensembles
• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.