# Ted Cox : Cutoff for the noisy voter model

Given a continuous time Markov Chain \( q(x,y)\) on a
finite set *S*, the associated noisy voter model is the
continuous time Markov chain on \(\{0,1\}^S\) which evolves
by (i) for each two sites x and y in *S*, the state at
site x changes to the value of the state at site
y at rate \( q(x,y) \) and (ii) each site rerandomizes
its state at rate 1. We show that if there is a uniform
bound on the rates \(q(x,y)\) and the corresponding
stationary distributions are ``almost'' uniform, then the
mixing time has a sharp cutoff at time \(\log |S|/2\) with a
window of order 1. Lubetzky and Sly proved cutoff with a
window of order 1 for the stochastic Ising model on
toroids: we obtain the special case of their result for
the cycle as a consequence of our result.

**Category**: Probability**Duration**: 01:34:46**Date**: March 3, 2016 at 4:25 PM**Views**: 112-
**Tags:**seminar, Probability Seminar

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