V Encontro da Pós-Graduação em Matemática da UFBA 20 a 24 de novembro de 2017

Spectral Gap of Markov Chains via Comparison of Dirichlet Forms Pedro Cardoso, Tertuliano Franco

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Abstract The aim of this master’s thesis is to study some results with respect to the spectral gap of reversible Markov chains; the main tool will be Dirichlet forms. For finite chains, we present some techniques that give bounds on the eigenvalues in order to estimate the spectral gap. For symmetric zero-range processes satisfying some conditions, we achieve a spectral gap of order n−2 on a cube of volume nd .

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e-mail: [email protected], [email protected]

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