When the geodesic becomes rigid in the directed landscape

Abstract

When the value $L$ of the directed landscape at a point $(\mathbf{p};\mathbf{q})$ is sufficiently large, the geodesic from $\mathbf{p}$ to $\mathbf{q}$ is rigid and its location fluctuates of order $L^{-1/4}$ around its expectation. We further show that at a midpoint of the geodesic, the location of the geodesic and the value of the directed landscape after appropriate scaling converge to two independent Gaussians.

13 pages, 1 figure

References in corpus (4)

• Asymptotics in ASEP with Step Initial Condition
• The directed landscape
• Exponents governing the rarity of disjoint polymers in Brownian last passage percolation
• Three-halves variation of geodesics in the directed landscape