Spectrum of large random reversible Markov chains: two examples

zbMath1276.15016arXiv0811.1097MaRDI QIDQ2865810

Djalil Chafaï, Charles Bordenave, Pietro Caputo

Publication date: 3 December 2013

Full work available at URL: https://arxiv.org/abs/0811.1097

zbMATH Keywords

random walkshomogenizationrandom matricesspectral gaprandom environmentspectral analysistridiagonal matricesreversible Markov chainsWigner's semi-circle lawarc-sine lawbirth-and death processes

Mathematics Subject Classification ID

Multivariate analysis (62H99) Strong limit theorems (60F15) Processes in random environments (60K37) Random matrices (algebraic aspects) (15B52) Generation, random and stochastic difference and differential equations (37H10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (10)

Tridiagonal random matrix: Gaussian fluctuations and deviations ⋮ Circular law theorem for random Markov matrices ⋮ Spectral norm bounds for block Markov chain random matrices ⋮ Singular value distribution of dense random matrices with block Markovian dependence ⋮ Spectrum of large random Markov chains: Heavy-tailed weights on the oriented complete graph ⋮ Spectrum of non-Hermitian heavy tailed random matrices ⋮ Clustering in block Markov chains ⋮ Low eigenvalues of Laplacian matrices of large random graphs ⋮ Spectrum of large random reversible Markov chains: heavy-tailed weights on the complete graph ⋮ The spectral gap of sparse random digraphs

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