Exactly solving the KPZ equation

Ivan Corwin

Exactly solving the KPZ equation

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arxiv 1804.05721 v1 pith:7KS2HA3Z submitted 2018-04-16 math.PR

Ivan Corwin This is my paper

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keywords equationexactlycompletedistributionexactformulahopf-coleintended

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We present a complete proof of the exact formula for the one-point distribution for the narrow-wedge Hopf-Cole solution to the Kardar-Parisi-Zhang (KPZ) equation. This presentation is intended to be self-contained so no previous knowledge about stochastic PDEs, or exactly solvable systems is presumed.

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The half-space KPZ line ensemble and its scaling limit
math.PR 2025-06 conditional novelty 7.0 of 10

The half-space KPZ line ensemble is constructed, proven tight under 1:2:3 scaling in critical and supercritical regimes, and shown to have subsequential limits with a one-sided Gibbs property, including pairwise pinne...

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