Eigenvalue bounds on restrictions of reversible nearly uncoupled Markov chains
type: Item
instance of: scholarly article
title: Eigenvalue bounds on restrictions of reversible nearly uncoupled Markov chains
zbMATH Open document ID: 1076.15018
author: Eike Meerbach
author: Christof Schütte
author: Alexander Fischer
published in: Linear Algebra and its Applications
publication date: 2005-05-04T00:00:00Z
review text: The authors analyze decompositions of reversible nearly uncoupled Markov chains into rapid mixing subchains, presenting upper bounds on the second eigenvalue for restriction and stochastic complementation chains of reversible Markov chains as well as a relation between them. The authors also illustrate the obtained bounds analytically for bunkbed graphs, and apply the to restricted Markov chains that arise when analyzing comformation dynamics of a small biomolecule. The efficiency of applying an uncoupling-coupling technique to a nearly uncoupled Markov chain essentially depends on the second eigenvalues of the resulting subchain which is bounded far away from \(1\). The main theorems of this article provide bounds on this spectral gap. The theorem may help better understand the structure and similarities of uncoupled chains to the original Markov chain and thus shed some light on the usefulness and applicability of uncoupling-coupling techniques.
reviewed by: Huang Wenxue
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 2165377
zbMATH Keywords: biomolecules
zbMATH Keywords: confirmation dynamics
zbMATH Keywords: Markov chains
zbMATH Keywords: rapid mixing
zbMATH Keywords: stationary distribution
zbMATH Keywords: stochastic complementation
zbMATH Keywords: uncoupling-coupling
zbMATH Keywords: stochastic matrices
zbMATH Keywords: eigenvalue bounds
zbMATH Keywords: eigenvalue
MaRDI profile type: Publication
full work available at URL: j.laa.2004.10.018
OpenAlex ID: W2094375648
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DOI: 10.1016/J.LAA.2004.10.018
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description: scientific article; zbMATH DE number 2165377