CLT for real \(\beta\)-ensembles at high temperature

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31) Spectral theory of functional-differential operators (34K08)

Cites Work

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Asymptotic expansion of a partition function related to the sinh-model
Fluctuations of linear eigenvalue statistics of \(\beta \) matrix models in the multi-cut regime
Tracy-Widom at high temperature
Poisson statistics for matrix ensembles at large temperature
A simple proof of the Poincaré inequality for a large class of probability measures
About the stationary states of vortex systems
Diffusing particles with electrostatic repulsion
Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics
Mesoscopic central limit theorem for general \(\beta\)-ensembles
CLT for fluctuations of \(\beta \)-ensembles with general potential
Fluctuations of two dimensional Coulomb gases
Asymptotic expansion of \(\beta \) matrix models in the one-cut regime
On fluctuations of eigenvalues of random Hermitian matrices.
Concentration inequality around the thermal equilibrium measure of Coulomb gases
Thermal approximation of the equilibrium measure and obstacle problem
Optimal local law and central limit theorem for \(\beta\)-ensembles
Large deviations for Gibbs ensembles of the classical Toda chain
Poisson statistics for beta ensembles on the real line at high temperature
Generalized Gibbs ensembles of the classical Toda chain
CLT for circular beta-ensembles at high temperature
Free transport-entropy inequalities for non-convex potentials and application to concentration for random matrices
Quantitative normal approximation of linear statistics of \(\beta \)-ensembles
Large deviations principle for the largest eigenvalue of the Gaussian \(\beta \)-ensemble at high temperature
A large deviation principle for empirical measures on Polish spaces: application to singular Gibbs measures on manifolds
Transport maps for \(\beta\)-matrix models and universality
Maximal inequalities and Riesz transform estimates on \(L^p\) spaces for Schrödinger operators with nonnegative potentials
Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients
An Introduction to Random Matrices
Weighted Sobolev spaces
Matrix models for beta ensembles
Change of variables as a method to study general β-models: Bulk universality
Asymptotics of Random Matrices and Related Models
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
Gaussian fluctuations and free energy expansion for Coulomb gases at any temperature
Large deviations for Ablowitz-Ladik lattice, and the Schur flow
Local laws and a mesoscopic CLT for β‐ensembles
Generalized transport inequalities and concentration bounds for Riesz-type gases

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