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Richard Durrett : Life and Death on a Random Graph

At the turn of this century it was realized that social and communication networks were best modeled by graphs that were "small worlds" and/or had power law degree distributions. I will discuss two examples. The first is a situation where physicist's mean field arguments give the wrong answer about the spread of epidemic. The second, inspired by a gypsy moth outbreak in the late 1980s in NY leads to chaotic behavior. I will concentrate on what is true rather than why, so the talk should be accessible to a wide audience.

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