Upper tail large deviations of the directed landscape

Sayan Das; Duncan Dauvergne; Bálint Virág

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arXiv · 2405.14924

Upper tail large deviations of the directed landscape

Sayan Das·Duncan Dauvergne·Bálint Virág

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Abstract

Starting from one-point tail bounds, we establish an upper tail large deviation principle for the directed landscape at the metric level. Metrics of finite rate are in one-to-one correspondence with measures supported on a set of countably many paths, and the rate function is given by a certain Kruzhkov entropy of these measures. As an application of our main result, we prove a large deviation principle for the directed geodesic.

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BibTeX RIS

Sayan Das, Duncan Dauvergne, Bálint Virág. 2024-05-23. Upper tail large deviations of the directed landscape. https://arxiv.org/abs/2405.14924

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