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### Uniqueness of the Friend Cluster in the Social Network Model on Non-amenable Regular Graphs

**Student-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.