When the geodesic becomes rigid in the directed landscape

2021/06/13 by Zhipeng Liu, Liu, Zhipeng · 1 citation
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2106.06913

openalex publication_date 2021/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

When the value L of the directed landscape at a point (p;q) is sufficiently large, the geodesic from p to 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.

Citations

• The KPZ fixed point
• The directed landscape

Cited by

• Limiting one-point fluctuations of the geodesic in the directed landscape near the endpoints when the geodesic length goes to infinity

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