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2014 Mixing under monotone censoring
Jian Ding, Elchanan Mossel
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Electron. Commun. Probab. 19: 1-6 (2014). DOI: 10.1214/ECP.v19-3157


We initiate the study of mixing times of Markov chain under monotone censoring. Suppose we have some Markov Chain $M$ on a state space $\Omega$ with stationary distribution $\pi$ and a monotone set $A \subset \Omega$. We consider the chain $M'$ which is the same as the chain $M$ started at some $x \in A$ except that moves of $M$ of the form $x \to y$ where $x \in A$ and $y \notin A$ are {\em censored} and replaced by the move $x \to x$. If $M$ is ergodic and $A$ is connected, the new chain converges to $\pi$ conditional on $A$. In this paper we are interested in the mixing time of the chain $M'$ in terms of properties of $M$ and $A$. Our results are based on new connections with the field of property testing. A number of open problems are presented.


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Jian Ding. Elchanan Mossel. "Mixing under monotone censoring." Electron. Commun. Probab. 19 1 - 6, 2014.


Accepted: 20 July 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1317.60087
MathSciNet: MR3233208
Digital Object Identifier: 10.1214/ECP.v19-3157

Primary: 60G15
Secondary: 60G70

Keywords: mixing time , testing monotonicity


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