Noncrossing partitions, Catalan words, and the semicircle law

DOI10.1007/s10959-011-0365-4zbMath1279.60011OpenAlexW1972571531MaRDI QIDQ354756

Arup Bose, Sayan Banerjee

Publication date: 19 July 2013

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-011-0365-4

zbMATH Keywords

eigenvaluesrandom matricescirculant matricesmethod of momentsnoncrossing partitionsempirical spectral distributionasymptotic freenessCatalan wordsHankel random matricespatterned random matricesToeplitz random matricesWigner semicircle law

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Partitions of sets (05A18) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Convergence of probability measures (60B10)

Related Items (9)

The limiting spectral measure for ensembles of symmetric block circulant matrices ⋮ Distribution of eigenvalues of highly palindromic Toeplitz matrices ⋮ Largest eigenvalue of large random block matrices: A combinatorial approach ⋮ Limiting Spectral Distributions of Families of Block Matrix Ensembles ⋮ Spectral analysis of large block random matrices with rectangular blocks ⋮ Spectral statistics of non-Hermitian random matrix ensembles ⋮ Random matrix ensembles with split limiting behavior ⋮ Bulk behaviour of some patterned block matrices ⋮ Spectral distributions of periodic random matrix ensembles

Cites Work

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• Convergence of joint moments for independent random patterned matrices
• On the distribution of the roots of certain symmetric matrices
• The spectral laws of Hermitian block-matrices with large random blocks
• Another look at the moment method for large dimensional random matrices
• Limit laws for random matrices and free products
• An Introduction to Random Matrices

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