Can I read Liouville First-passage Percolation: Subsequential Scaling Limits at High Temperature on EtoBox?

Liouville First-passage Percolation: Subsequential Scaling Limits at High Temperature by Ding, Jian; Dunlap, Alexander is a scholarly article available to read on EtoBox.

What is Liouville First-passage Percolation: Subsequential Scaling Limits at High Temperature about?

Let $\{Y_{\mathfrak{B}}(x)\,:\,x\in\mathfrak{B}\}$ be a discrete Gaussian free field in a two-dimensional box $\mathfrak{B}$ of side length $S$ with Dirichlet boundary conditions. We study Liouville first-passage percolation: the shortest-path metric in which each vertex $x$ is given a weight of $e^{\gamma Y_{\mathfrak{B}}(x)}$ for some $\gamma>0$. We show that for sufficiently small but fixed $\gamma>0$, for any sequence of scales $\{S_{k}\}$ there exists a subsequence along which the appropriately scaled and interpolated Liouville FPP metric converges in the Gromov--Hausdorff sense to a random metric on the unit square in $\mathbf{R}^{2}$. In addition, all possible (conjecturally unique) scaling limits are homeomorphic by bi-H\"older-continuous homeomorphisms to the unit square with the Euclidean metric.

Author

Ding, Jian; Dunlap, Alexander

Published

2016

Language

EN