Liouville first passage percolation: geodesic dimension is strictly larger than 1 at high temperatures
主 题: Liouville first passage percolation: geodesic dimension is strictly larger than 1 at high temperatures
报告人: 章复熹 副教授 (北京大学)
时 间: 2016-10-24 15：00-16：00
地 点: 北京大学理科一号楼 1303（概率论系列报告）
We consider a discrete Gaussian free field h in a two-dimensional box of side length N with Dirichlet boundary conditions. We study the Liouville first passage percolation, i.e., the shortest path metric where each vertex is given a weight of exp(\gamma h) for some positive parameter \gamma. We show that for sufficiently small but fixed gamma, with probability tending to 1 as N goes to \infty, the dimensions of all geodesics between vertices of macroscopic distances are simultaneously strictly larger than 1.