Matrix addition and the Dunkl transform at high temperature

DOI10.1007/s00220-022-04411-zzbMath1495.60004arXiv2105.03795OpenAlexW3161310444MaRDI QIDQ2165046

Vadim Gorin, Cesar Cuenca, Florent Benaych-Georges

Publication date: 18 August 2022

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

Full work available at URL: https://arxiv.org/abs/2105.03795

zbMATH Keywords

Dunkl transformdeformed cumulants

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Strong limit theorems (60F15) Random matrices (algebraic aspects) (15B52) Convergence of probability measures (60B10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Cites Work

• Moments of the position of the maximum for GUE characteristic polynomials and for log-correlated Gaussian processes
• Free probability and random matrices
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Multilevel Dyson Brownian motions via Jack polynomials
• The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles
• Poisson statistics for matrix ensembles at large temperature
• Eigenvalue statistics for CMV matrices: From Poisson to clock via random matrix ensembles
• The combinatorics of associated Hermite polynomials
• Limit laws for random matrices and free products
• Mackey analysis of infinite classical motion groups
• Shifted Jack polynomials, binomial formula, and applications
• Large deviations for Wigner's law and Voiculescu's non-commutative entropy
• Orthogonal polynomials and special functions. Notes for the lectures of the summer school, Leuven, Belgium, August 12--16, 2002
• Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics
• Cumulants for finite free convolution
• Macdonald-positive specializations of the algebra of symmetric functions: proof of the Kerov conjecture
• Fluctuations of particle systems determined by Schur generating functions
• Some combinatorial properties of Jack symmetric functions
• Superconvergence to the central limit and failure of the Cramér theorem for free random variables
• On fluctuations of eigenvalues of random Hermitian matrices.
• Beta Laguerre ensembles in global regime
• Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions
• Generalized Gibbs ensembles of the classical Toda chain
• CLT for circular beta-ensembles at high temperature
• Law of large numbers and central limit theorems through Jack generating functions
• Beta Jacobi ensembles and associated Jacobi polynomials
• The high temperature crossover for general 2D Coulomb gases
• Fourier transform on high-dimensional unitary groups with applications to random tilings
• Representations of classical Lie groups and quantized free convolution
• From sine kernel to Poisson statistics
• Markov–Krein transform
• General β-Jacobi Corners Process and the Gaussian Free Field
• A Short Proof of Selberg’s Generalized Beta Formula
• Associated Laguerre and Hermite polynomials
• Lectures on the Combinatorics of Free Probability
• Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models
• Differential-Difference Operators Associated to Reflection Groups
• Lectures on affine Hecke algebras and Macdonald’s conjectures
• An Introduction to Dunkl Theory and Its Analytic Aspects
• Rayleigh triangles and non-matrix interpolation of matrix beta integrals
• Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators
• A positive radial product formula for the Dunkl kernel
• Recursive construction for a class of radial functions. I. Ordinary space
• Invariant β-Wishart ensembles, crossover densities and asymptotic corrections to the Marčenko–Pastur law
• Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials
• The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain
• Universal Behavior of the Corners of Orbital Beta Processes
• Gaussian fluctuations for products of random matrices
• The boundary of the orbital beta process
• Crystallization of Random Matrix Orbits
• Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Matrix addition and the Dunkl transform at high temperature