Segregating Markov Chains
Journal article, 2018

Dealing with finite Markov chains in discrete time, the focus often lies on convergence behavior and one tries to make different copies of the chain meet as fast as possible and then stick together. There are, however, discrete finite (reducible) Markov chains, for which two copies started in different states can be coupled to meet almost surely in finite time, yet their distributions keep a total variation distance bounded away from 0, even in the limit as time tends to infinity. We show that the supremum of total variation distance kept in this context is .

Markov chain

Total variation distance

Non-Markovian coupling

Coupling inequality


Timo Hirscher


Anders Martinsson

Chalmers, Mathematical Sciences, Algebra and geometry

Journal of Theoretical Probability

0894-9840 (ISSN) 1572-9230 (eISSN)

Vol. 31 3 1512-1538

Subject Categories

Computational Mathematics

Transport Systems and Logistics

Control Engineering



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