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Masha Bessonov : The Voter Model

We'll look at a random process on the integer lattice $/mathbb{Z}^2$ known as the voter model. Let's suppose that each point on the lattice represents a single household with one voter who holds one of two possible opinions, 0 or 1 (e.g. Republican or Democrat). Starting with an initial configuration of 0's and 1's on $/mathbb{Z}^2$, a voter changes their opinion at a rate proportional to the number of neighbors holding a different opinion. I'll demonstrate a clever and useful approach to analysing the voter model via the dual process. We'll be able to determine whether or not our process has any nontrivial stationary distributions. I'll also briefly discuss the newest research on variants of the voter model.

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