Cutoff for the noisy voter model
Artikel i vetenskaplig tidskrift, 2016

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.

Mathematics

mixing times for Markov chains

Noisy voter models

ising-model

cutoff phenomena

Författare

J. T. Cox

Syracuse University

Y. Peres

Jeffrey Steif

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Annals of Applied Probability

1050-5164 (ISSN)

Vol. 26 2 917-932

Ämneskategorier

Matematik

DOI

10.1214/15-aap1108

Mer information

Skapat

2017-10-07