Student Probability Seminar

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Global Solution for Burgers Equation and Its Connection with Geodesics in First-Passage Percolation

Speaker: Liying Li

Location: Warren Weaver Hall 1314

Date: Thursday, November 12, 2015, 2 p.m.

Synopsis:

In this talk I will explain how to construct skew-invariant global solution for 1D Burgers equation with Poisson random forcing. After writing down the variational formula for the solution, we can make use of several results about geodesics in poissonian point field. In particular, infinite geodesics exist and each of them has an asymptotic slope, and also every two geodesics with the same asymptotic slope almost surely coalesce. The key step is a concentration inequality for action which handles the non-compactness of our domain and also gives an upper bound for the fluctuation exponent. In the end I might talk about some similar results for positive viscosity.