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**Harvard**

Cox, J., Peres, Y. och Steif, J. (2016) *Cutoff for the noisy voter model*.

** BibTeX **

@article{

Cox2016,

author={Cox, J. T. and Peres, Y. and Steif, Jeffrey},

title={Cutoff for the noisy voter model},

journal={Annals of Applied Probability},

issn={1050-5164},

volume={26},

issue={2},

pages={917-932},

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 in the following way: (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); (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 vertical bar S vertical bar/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={2016},

keywords={Noisy voter models; mixing times for Markov chains; cutoff phenomena; ising-model; Mathematics},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 237139

A1 Cox, J. T.

A1 Peres, Y.

A1 Steif, Jeffrey

T1 Cutoff for the noisy voter model

YR 2016

JF Annals of Applied Probability

SN 1050-5164

VO 26

IS 2

SP 917

OP 932

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 in the following way: (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); (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 vertical bar S vertical bar/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

DO 10.1214/15-aap1108

LK http://dx.doi.org/10.1214/15-aap1108

LK http://publications.lib.chalmers.se/records/fulltext/237139/local_237139.pdf

OL 30