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Upper tail large deviations of the directed landscape
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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.
Forward citations
Cited by 2 Pith papers
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An upper tail field of the KPZ fixed point
A newly constructed 'upper tail field' is the local limit of the KPZ fixed point near a conditioned large value, interpolating between Brownian and KPZ scaling regimes.
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For general i.i.d. weights, the midpoint of the geodesic between (0,0) and (n,n) lying at position n/2+tn has probability e^{-2nJ_t(μ0)+o(n)}.
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