Large deviation principles via spherical integrals

DOI10.2140/pmp.2022.3.543OpenAlexW4287814831MaRDI QIDQ2693722

Jiaoyang Huang, Serban Teodor Belinschi, Alice Guionnet

Publication date: 24 March 2023

Published in: Probability and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07117

zbMATH Keywords

random matricesLittlewood-Richardson coefficientsempirical measureslarge deviation principlesspherical integral

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Symmetric functions and generalizations (05E05) Large deviations (60F10)

Related Items

Asymptotics of rectangular spherical integrals ⋮ Projections of orbital measures and quantum marginal problems

Cites Work

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• Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails
• The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
• A Fourier view on the \(R\)-transform and related asymptotics of spherical integrals
• Universality of random matrices and local relaxation flow
• Spectrum of non-Hermitian heavy tailed random matrices
• On the distribution of the roots of certain symmetric matrices
• Corank-1 projections and the randomised Horn problem
• Large deviations for the largest eigenvalue of Rademacher matrices
• Large deviations and stochastic calculus for large random matrices
• Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix
• Eigenvalues of sums of Hermitian matrices
• The eigenvalues of random symmetric matrices
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Addendum to ``On the variation in the cohomology of the symplectic form of the reduced phase space
• Convexity properties of the moment mapping
• Limit laws for random matrices and free products
• Stable bundles, representation theory and Hermitian operators
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• Level-spacing distributions and the Airy kernel
• Level spacing distributions and the Bessel kernel
• Large deviations for Wigner's law and Voiculescu's non-commutative entropy
• First order asymptotics of matrix integrals; a rigorous approach towards the understanding of matrix models
• Universality at the edge of the spectrum in Wigner random matrices.
• Large deviations asymptotics for spherical integrals
• Horn's problem and Harish-Chandra's integrals. Probability density functions
• Horn's problem and Fourier analysis
• Fixed energy universality of Dyson Brownian motion
• Planar diagrams
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• Addendum to: Large deviations asymptotics for spherical integrals
• Random matrices: Universality of local eigenvalue statistics up to the edge
• Large deviations for the largest eigenvalue of the sum of two random matrices
• On Horn's problem and its volume function
• A variant of Horn's problem and the derivative principle
• Asymptotics of unitary multimatrix models: the Schwinger-Dyson lattice and topological recursion
• Asymptotics of unitary and orthogonal matrix integrals
• On the largest Kronecker and Littlewood-Richardson coefficients
• Brownian Gibbs property for Airy line ensembles
• A necessary and sufficient condition for edge universality of Wigner matrices
• The Horn problem for real symmetric and quaternionic self-dual matrices
• Large deviations for the largest eigenvalue of sub-Gaussian matrices
• Linear functionals of eigenvalues of random matrices
• Fixed Energy Universality for Generalized Wigner Matrices
• Free Random Variables
• Fullness, Connes’ $\chi $-groups, and ultra-products of amalgamated free products over Cartan subalgebras
• INVARIANT DIFFERENTIAL OPERATORS ON A SEMISIMPLE LIE ALGEBRA
• Invariant measure on sums of symmetric 3*3 matrices with specified eigenvalues
• Bulk universality for Wigner matrices
• An Introduction to Random Matrices
• Convexity and Commuting Hamiltonians
• On convexity, the Weyl group and the Iwasawa decomposition
• Central limit theorem for traces of large random symmetric matrices with independent matrix elements
• Large deviations from the circular law
• The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
• On the free convolution with a semi-circular distribution
• The planar approximation. II
• Universality of local spectral statistics of random matrices
• Eigenvalues, invariant factors, highest weights, and Schubert calculus
• On Schur problem and Kostka numbers
• Revisiting Horn’s problem
• An elementary proof of the triangle inequality for the Wasserstein metric
• The Plemelj distributional formulas
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix
• Duistermaat–Heckman measure and the mixture of quantum states
• Aging of spherical spin glasses