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Math Colloquium
Arjun Krishan University of Utah Title: Stochastic Homogenization and First-Passage Percolation Abstract: First-passage percolation is a random growth model on the cubic lattice Z^d. It models, for example, the spread of fluid in a random porous medium. This talk is about the asymptotic behavior of the first-passage time T(x), which represents the time it takes for a fluid particle released at the origin to reach a point x on the lattice.The first-order asymptotic --- the law of large numbers --- for T(x) as x goes to infinity in a particular direction u, is given by a deterministic function of u called the time-constant. The first part of the talk will focus on a new variational formula for the time-constant, which results from a connection between first-passage percolation and stochastic homogenization for discrete Hamilton-Jacobi-Bellman equations.The second-order asymptotic of the first-passage time describes its fluctuations; i.e., the analog of the central limit theorem for T(x). In two dimensions, the fluctuations are (conjectured to be) in the Kardar-Parisi-Zhang (KPZ) or random matrix universality class. We will present some new results (with J. Quastel) in the direction of the KPZ universality conjecture.Date: Friday, January 22, 2016Time: 4:30 pmLocation: Wean Hall 7500Submitted by: BohmanNote: Refreshments at 4:00 pm, Wean Hall 6220 |