On fluctuations of eigenvalues of random permutation matrices

DOI10.1214/13-AIHP569zbMath1323.60013arXiv1106.2108MaRDI QIDQ2346189

Kim Dang, Gérard Ben Arous

Publication date: 29 May 2015

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2108

zbMATH Keywords

random matricesinfinitely divisible distributionsrandom permutationslinear eigenvalue statisticstrapezoidal approximations

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Combinatorial probability (60C05) Random matrices (algebraic aspects) (15B52) Numerical integration (65D30) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (9)

On a limiting point process related to modified permutation matrices ⋮ Cycles and eigenvalues of sequentially growing random regular graphs ⋮ On smooth mesoscopic linear statistics of the eigenvalues of random permutation matrices ⋮ Global eigenvalue fluctuations of random biregular bipartite graphs ⋮ The characteristic polynomial of a random permutation matrix at different points ⋮ Random permutation matrices under the generalized Ewens measure ⋮ On the number of eigenvalues of modified permutation matrices in mesoscopic intervals ⋮ Central limit theorems for linear statistics of heavy tailed random matrices ⋮ Exchangeable pairs, switchings, and random regular graphs

Cites Work

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• Functional limit theorems for random regular graphs
• Sparse regular random graphs: spectral density and eigenvectors
• Gaussian fluctuations for non-Hermitian random matrix ensembles
• Characterization of the speed of convergence of the trapezoidal rule
• Fluctuations of eigenvalues and second order Poincaré inequalities
• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Some limit theorems for the eigenvalues of a sample covariance matrix
• The cycle structure of random permutations
• Poisson process approximations for the Ewens sampling formula
• Models for the logarithmic species abundance distributions
• On random matrices from the compact classical groups
• Logarithmic combinatorial structures: A probabilistic approach
• On the statistical mechanics approach in the random matrix theory: Integrated density of states.
• Eigenvalue distributions of random unitary matrices
• Eigenvalue distributions of random permutation matrices.
• The characteristic polynomial of a random permutation matrix.
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• Random permutation matrices under the generalized Ewens measure
• On fluctuations of eigenvalues of random Hermitian matrices.
• The sampling theory of selectively neutral alleles
• Linear functionals of eigenvalues of random matrices
• The kernel of a rule of approximate integration
• Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models
• Limiting laws of linear eigenvalue statistics for Hermitian matrix models
• Limit Theorems for Combinatorial Structures via Discrete Process Approximations
• A Rate for the Erdős-Turán Law
• On the Eigenvalues of Random Matrices
• Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture
• Asymptotic properties of large random matrices with independent entries
• Ordered Cycle Lengths in a Random Permutation
• On the completeness of Lambert functions

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