Probability Seminar
Thursday, March 3, 2016, 4:30pm, 119 Physics
Ted Cox (Syracuse)
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 (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. [video]

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