A necessary and sufficient condition for double coset lumping of Markov chains on groups with an application to the random to top shuffle

DOI10.1090/PROC/16853zbMATH Open1545.60004MaRDI QIDQ6566378

John R. Britnell, Mark Wildon

Publication date: 3 July 2024

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Markov chains on groupsdouble coset lumping

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Sums of independent random variables; random walks (60G50) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Eigenvalues, singular values, and eigenvectors (15A18) Stochastic matrices (15B51) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Probabilistic methods in group theory (20P05)

Cites Work

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• Bell numbers, partition moves and the eigenvalues of the random-to-top shuffle in Dynkin types A, B and D
• The bias of three pseudo-random shuffles
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• Random walks and hyperplane arrangements
• Comparison theorems for reversible Markov chains
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• Statistical enumeration of groups by double cosets
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• Involutive random walks on total orders and the anti-diagonal eigenvalue property
• On the matrix occurring in a linear search problem
• Analysis of Top To Random Shuffles
• Convergence Rates for Markov Chains
• The hit-and-run version of top-to-random
• Double coset Markov chains

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