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Uniqueness of the Friend Cluster in the Social Network Model on Non-amenable Regular GraphsStudent-Run Applied & Math Seminar
|Speaker: ||Chuan Qin, University of California, Davis|
|Location: ||2112 MSB|
|Start time: ||Fri, Mar 15 2013, 12:10PM|
We consider the following model of a social network, in which
people move on an infinite regular graph G and make friends. For each
vertex x in G, there are initially N(x) people at x, where N(x)'s are
i.i.d. Poisson random variables with mean $\lambda$. Each person performs a
discrete-time simple random walk, independently of others. Whenever two
people meet at a vertex, they befriend each other and each other's friends.
We answer the following question asked by Itai Benjamini: For what values
of $\lambda$ is it true that every pair of people eventually become friends
with probability 1?
We will provide pizzas and soda for lunch.