Spectrum of large random reversible Markov chains: two examples

Abstract

We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior at the edge, including the so called spectral gap. Results are obtained for two simple models with distinct limiting features. The first model is built on the complete graph while the second is a birth-and-death dynamics. Both models give rise to random matrices with non independent entries.

accepted in ALEA, March 2010

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Cited by in corpus (4)

• Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph
• The Dirichlet Markov Ensemble
• Singular value distribution of dense random matrices with block Markovian dependence
• Spectral analysis of 1D nearest-neighbor random walks and applications to subdiffusive trap and barrier models