Percolation on the stationary distribution of the voter model on Z^d – Daniel Valesin

Daniel Valesin
University of Groningen

Date(s) : 27/03/2015   iCal
11 h 00 min - 12 h 00 min

The voter model on $\Z^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When the model is considered in dimension 3 or higher, its set of (extremal) stationary distributions is equal to a family of measures $\mu_\alpha$, for $\alpha$ between 0 and 1. A configuration sampled from $\mu_alpha$ is a field of 0’s and 1’s on $\Z^d$ in which the density of 1’s is $\alpha$. We consider such a configuration from the point of view of site percolation on $\Z^d$. We prove that in dimensions 5 and higher, the probability of existence of an infinite percolation cluster exhibits a phase transition in $\alpha$. If the voter model is allowed to have long range, we prove the same result for dimensions 3 and higher. Joint work with Balázs Ráth.


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