Eigenvalue distributions of random permutation matrices.

DOI10.1214/aop/1019160498zbMath1044.15017OpenAlexW1987235976MaRDI QIDQ1872159

Kelly Wieand

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1019160498

zbMATH Keywords

permutationsrandom matrices

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Combinatorial probability (60C05) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Related Items (19)

On a limiting point process related to modified permutation matrices ⋮ The characteristic polynomial of a random permutation matrix. ⋮ Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture ⋮ The Dirichlet Markov ensemble ⋮ On Statistics of Permutations Chosen From the Ewens Distribution ⋮ On a Flow of Operators Associated to Virtual Permutations ⋮ Functional limit theorems for random regular graphs ⋮ The distribution of eigenvalues of randomized permutation matrices ⋮ Spectral statistics of permutation matrices ⋮ Cycles and eigenvalues of sequentially growing random regular graphs ⋮ On smooth mesoscopic linear statistics of the eigenvalues of random permutation matrices ⋮ Random permutation matrices under the generalized Ewens measure ⋮ On averages of randomized class functions on the symmetric groups and their asymptotics ⋮ On the number of eigenvalues of modified permutation matrices in mesoscopic intervals ⋮ The Poisson distribution for linear statistics of random permutations ⋮ Sharp bounds for the variance of linear statistics on random permutations ⋮ Aspects of large random Markov kernels ⋮ On fluctuations of eigenvalues of random permutation matrices ⋮ Optimal Ordering of Projections using Permutation Matrices and Angles between Projection Subspaces

Cites Work

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• High powers of random elements of compact Lie groups
• The cycle structure of random permutations
• Poisson process approximations for the Ewens sampling formula
• Level spacings distribution for large random matrices: Gaussian fluctuations
• The characteristic polynomial of a random permutation matrix.
• Limit Theorems for Combinatorial Structures via Discrete Process Approximations
• On the distribution of the length of the longest increasing subsequence of random permutations
• A Rate for the Erdős-Turán Law
• On the Eigenvalues of Random Matrices
• Ordered Cycle Lengths in a Random Permutation
• The fundamental limit theorems in probability

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