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On random walks and switched random walks on homogeneous spaces

Part of: Algebraic combinatorics Markov processes

Published online by Cambridge University Press:  28 November 2022

Elvira Moreno Open the ORCID record for Elvira Moreno [Opens in a new window]  and
Mauricio Velasco Open the ORCID record for Mauricio Velasco [Opens in a new window]
Elvira Moreno
Affiliation:
Computing and Mathematical Sciences, California Institute of Technology, Department of Computing and Mathematical Sciences, 1200 E. California Blvd., MC 305-16, Pasadena, CA 91125-2100, USA
Mauricio Velasco*
Affiliation:
Departamento DE Matemáticas, Universidad de los Andes, Carrera 1 No. 18a 10, Edificio H, Primer Piso, 111711 Bogotá, Colombia
*
*Corresponding author. Email: mvelasco@uniandes.edu.co
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Abstract

We prove new mixing rate estimates for the random walks on homogeneous spaces determined by a probability distribution on a finite group $G$ . We introduce the switched random walk determined by a finite set of probability distributions on $G$ , prove that its long-term behaviour is determined by the Fourier joint spectral radius of the distributions, and give Hermitian sum-of-squares algorithms for the effective estimation of this quantity.

Keywords

Mixing ratesRandom walksSwitched random walksJoint spectral radiusHermitian polynomial norms

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 05E10: Combinatorial aspects of representation theory
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 32 , Issue 3 , May 2023 , pp. 398 - 421
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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