The smallest eigenvalue for reversible Markov chains

DOI10.1016/j.laa.2003.12.007zbMath1043.60057OpenAlexW2063062879MaRDI QIDQ1826846

Xiao Dong Zhang

Publication date: 6 August 2004

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2003.12.007

zbMATH Keywords

EigenvalueGraphReversible Markov chain

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (5)

Universality of cutoff for graphs with an added random matching ⋮ Covariance structure behind breaking of ensemble equivalence in random graphs ⋮ Constructing optimal transition matrix for Markov chain Monte Carlo ⋮ The normalized Laplacian spectrum of subdivisions of a graph ⋮ On the spectrum of the normalized Laplacian of iterated triangulations of graphs

Cites Work

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• Geometric bounds for eigenvalues of Markov chains
• Eigenvalues and expanders
• Computing the stationary distribution for infinite Markov chains
• A Markov chain on the symmetric group and Jack symmetric functions
• Comparing eigenvalue bounds for Markov chains: When does Poincaré beat Cheeger?
• On the rate of convergence of the Metropolis algorithm and Gibbs sampler by geometric bounds
• On the Convergence of Reversible Markov Chains
• A characterization of the smallest eigenvalue of a graph
• Geometric Approaches to the Estimation of the Spectral Gap of Reversible Markov Chains

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