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Strong stationary times and eigenvalues

Part of: Markov processes Basic linear algebra

Published online by Cambridge University Press:  14 July 2016

Peter Matthews
Peter Matthews*
Affiliation:
University of Maryland Baltimore County
*
∗ Postal address: Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21228, USA.
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Abstract

This note gives a new strong stationary time (SST) for reversible finite Markov chains. A modification of the initial distribution is represented as a mixture of distributions which have eigenvector interpretations, and for which good simple SSTs exist. This provides some insight into the relationship between SSTs and eigenvalues. Connections to duality and the threshold phenomenon are discussed.

Keywords

REVERSIBLE MARKOV CHAINSRATE OF CONVERGENCE TO STATIONARITY

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 228 - 233
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported by the National Security Agency under Grant Number MDA 904-88-H-2014.

References

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