The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain

DOI10.1063/5.0048481zbMath1469.60031arXiv2102.09201OpenAlexW3180154889MaRDI QIDQ5009755

G. Mazzuca, Peter J. Forrester

Publication date: 5 August 2021

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.09201

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Applications of statistics to physics (62P35) Random matrices (algebraic aspects) (15B52)

Related Items

Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schrödinger equation, On the mean density of states of some matrices related to the beta ensembles and an application to the Toda lattice, High–low temperature dualities for the classical β-ensembles, Matrix addition and the Dunkl transform at high temperature, Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular \(\beta\)-ensemble and double confluent Heun equation, Limit theorems and large deviations for \(\beta\)-Jacobi ensembles at scaling temperatures, Unified limits and large deviation principles for \(\beta\)-Laguerre ensembles in global regime, Limit theorems for moment processes of beta Dyson’s Brownian motions and beta Laguerre processes, Equilibrium spacetime correlations of the Toda lattice on the hydrodynamic scale, Preface to the Special Collection in Honor of Freeman Dyson, Large deviations for Ablowitz-Ladik lattice, and the Schur flow, A review of exact results for fluctuation formulas in random matrix theory, Dyson’s disordered linear chain from a random matrix theory viewpoint, Discrete integrable systems and random Lax matrices

Uses Software

• DLMF

Cites Work

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