# Junchi Li : New stochastic voting systems on fixed and random graphs

In this talk I will introduce two stochastic voting systems and results we proved. (i) Axelrod's model generalizes the voter model in which individuals have one of Q possible opinions about each of F issues and neighbors interact at a rate proportional to the fraction of opinions they share. We proved that on large two-dimensional torus if Q/F is small, then there is a giant component of individuals who share at least one opinion and consensus develops on this percolating cluster. (ii) The latent voter model allows a latent period after each site flips its opinion. We will present Shirshendu's result on a random r-regular graph with n vertices that as the rate of exponential latent period $\lambda \gg \log n$, dynamics converge to coexistence behavior with quasi-stationary density = 1/2 at $O(\lambda)$ times. Using different technologies one can generalize it to the varying degree case, a.k.a. the configuration models. Joint work with Rick Durrett and Shirshendu Chatterjee

**Category**: Graduate/Faculty Seminar**Duration**: 01:34:51**Date**: November 15, 2013 at 4:25 PM**Views**: 121-
**Tags:**seminar, Graduate/faculty Seminar

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