Student Probability Seminar

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Fluctuations in First-Passage Percolation

Speaker: Tom LaGatta

Location: Warren Weaver Hall 202

Date: Friday, April 1, 2011, 4:30 p.m.

Synopsis:

First-Passage Percolation is a model of random geometry on the lattice. In the 80s, Cox and Durrett proved a shape theorem for the model: balls under the random metric grow linearly in time. This is a geometric Law of Large Numbers and as such does not describe the fluctuations of balls from the limiting shape. Over the past thirty years, much has been proved about these fluctuations, but we are still very far from truly characterizing them. I will survey much of what has been proved and what is known, and discuss the vast gap between the two.