Planar First Passage Percolation

University Of Washington, Seattle WA

Investigators

Abstract

Probability theory has proven to be a useful framework for describing many systems that arise in statistical physics. These systems are often too complicated to model completely with any computer. Although exact computations are not possible, mathematics gives us a way to learn about some important properties of these systems. This research builds on recent advances in a model from physics known as first passage percolation. In addition to conducting mathematical research this award will help to develop the nation's scientific and technological infrastructure by supporting graduate and undergraduate education. Additionally it will sponsor several talks to help explain applications of mathematical research to a broader community. This research considers a large number of questions in first-passage percolation on the plane. Recently there have been great advances in the study of geodesics in first-passage percolation using Busemann functions. This research will build on these results to try to answer central questions in the field that have been open for decades. These questions include showing that the limiting shape in independent first-passage percolation is strictly convex and that there are no bi-infinite geodesics in any fixed direction. This project will help develop the nation's scientific and technological infrastructure by supporting graduate and undergraduate education.