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**Harvard**

Cox, T., Peres, Y. och Steif, J. (2015) * Cutoff for the noisy voter model *.

** BibTeX **

@unpublished{

Cox2015,

author={Cox, Ted and Peres, Yuval and Steif, Jeffrey},

title={ Cutoff for the noisy voter model },

abstract={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 (1) 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 (2) 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. Finally, we consider the model on a star and demonstrate
the surprising phenomenon that the time it takes for the chain started at all ones to become close in total
variation to the chain started at all zeros is of smaller order than the mixing time. },

year={2015},

keywords={noisy voter models, mixing times for Markov chains, cutoff phenomena},

note={16},

}

** RefWorks **

RT Unpublished Material

SR Electronic

ID 229076

A1 Cox, Ted

A1 Peres, Yuval

A1 Steif, Jeffrey

T1 Cutoff for the noisy voter model

YR 2015

AB 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 (1) 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 (2) 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. Finally, we consider the model on a star and demonstrate
the surprising phenomenon that the time it takes for the chain started at all ones to become close in total
variation to the chain started at all zeros is of smaller order than the mixing time.

LA eng

LK http://www.math.chalmers.se/~steif/p60.pdf

OL 30