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arXiv · 2609.39675

The starting point of a directed geodesic is special

Pantelis Tassopoulos·Sourav Sarkar
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Abstract

For any $t\in [0,1/2)$, consider the process $η_t:[0,1/2]\mapsto\mathbb{R}$ defined by $η_t(s)=Π(t+s)-Π(t)$, where $Π$ is the directed geodesic from $(0,0)$ to $(0,1)$ in the directed landscape. Let $0\leq t 0$. This proves Conjecture 14.5 in Dauvergne, Ortmann, and Virág, 2022 in the affirmative.

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Pantelis Tassopoulos, Sourav Sarkar. 2026-09-30. The starting point of a directed geodesic is special. https://arxiv.org/abs/2609.39675

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