One-point large deviations of the directed landscape geodesic

2025/03/12 by Daniel Spivak, Spivak, Daniel
Earth and Planetary Sciences · Environmental Science · Medicine · #Environmental Changes in China #FOS: Mathematics #FOS: Physical sciences #Geology and Paleoclimatology Research #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2503.09486

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

The directed landscape, the central object in the Kardar-Parisi-Zhang universality class, is shown to be the scaling limit of various models by Dauvergne and Virág (2022) and Dauvergne, Ortmann and Virág (2018). In his study of geodesics in upper tail deviations of the directed landscape, Liu (2022) put forward a conjecture about the rate of the lowest rate metric under which a geodesic between two points passes through a particular point between them. Das, Dauvergne and Virág (2024) disproved his conjecture, and made a conjecture of their own. This paper disproves that conjecture and puts the question to rest with an answer and a proof.

Related

• Upper tail large deviations of the directed landscape
• Limiting one-point fluctuations of the geodesic in the directed landscape near the endpoints when the geodesic length goes to infinity
• The 27 geodesic networks in the directed landscape
• When the geodesic becomes rigid in the directed landscape
• Non-existence of three non-coalescing infinite geodesics with the same direction in the directed landscape