@article{ECP3157,
author = {Jian Ding and Elchanan Mossel},
title = {Mixing under monotone censoring},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {19},
year = {2014},
keywords = {mixing time; testing monotonicity.},
abstract = {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.},
pages = {no. 46, 1-6},
issn = {1083-589X},
doi = {10.1214/ECP.v19-3157},
url = {http://ecp.ejpecp.org/article/view/3157}}