For more information about this meeting, contact Stephanie Zerby, Chun Liu, Amy Hanley.

Title: | First-passage percolation |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Arjun Krishnan, University of Utah |

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.
The analysis of this problem will involve tools and ideas from probability, PDEs, and ergodic theory. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 02 / 11 / 2016 |

Time: | 03:35pm - 04:35pm |