Asymptotic forms for hard and soft edge general \(\beta \) conditional gap probabilities

DOI10.1016/j.nuclphysb.2012.02.008zbMath1246.82037arXiv1110.4284OpenAlexW2086568064MaRDI QIDQ447326

Nicholas S. Witte, Peter J. Forrester

Publication date: 3 September 2012

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4284

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random matrices (algebraic aspects) (15B52) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31)

Related Items

Large deviations for the \(\operatorname{Sine}_\beta\) and \(\operatorname{Sch}_\tau\) processes, ASYMPTOTICS OF SPACING DISTRIBUTIONS AT THE HARD EDGE FOR β-ENSEMBLES, Linear differential equations for the resolvents of the classical matrix ensembles, Raney distributions and random matrix theory

Cites Work

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• Hard edge tail asymptotics
• Continuum limits of random matrices and the Brownian carousel
• Hermite and Laguerre \(\beta\)-ensembles: asymptotic corrections to the eigenvalue density
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• Asymptotics of the Airy-kernel determinant
• Large gaps between random eigenvalues
• Eigenvalue statistics for CMV matrices: From Poisson to clock via random matrix ensembles
• Level-spacing distributions and the Airy kernel
• Level spacing distributions and the Bessel kernel
• The spectrum edge of random matrix ensembles.
• A random matrix decimation procedure relating \(\beta = 2/( r + 1)\) to \(\beta = 2( r + 1)\)
• From random matrices to stochastic operators
• Large Deviations of Extreme Eigenvalues of Random Matrices
• Beta ensembles, stochastic Airy spectrum, and a diffusion
• Statistical Theory of the Energy Levels of Complex Systems. I
• Large deviations of the maximal eigenvalue of random matrices
• A simple derivation of the Tracy–Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix
• Higher-order analogues of the Tracy-Widom distribution and the Painlevé II hierarchy
• Hard and soft edge spacing distributions for random matrix ensembles with orthogonal and symplectic symmetry
• Large deviations of the maximum eigenvalue in Wishart random matrices
• Eigenvalues and Condition Numbers of Random Matrices
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Exact results and universal asymptotics in the Laguerre random matrix ensemble
• Asymptotics of level-spacing distributions for random matrices
• Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum
• Breakdown of universality in multi-cut matrix models
• Matrix models for beta ensembles
• Asymptotic level spacing of the Laguerre ensemble: a Coulomb fluid approach