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arXiv · 2210.13607

KPZ fluctuations in the planar stochastic heat equation

Jeremy Quastel·Alejandro Ramirez·Balint Virag
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Abstract

We use a version of the Skorokhod integral to give a simple and rigorous formulation of the Wick-ordered (stochastic) heat equation with planar white noise, representing the free energy of an undirected random polymer. The solution for all times is expressed as the L1 limit of a martingale given by the Feyman-Kac formula and defines a randomized shift, or Gaussian multiplicative chaos. The fluctuations far from the centre are shown to be given by the one-dimensional KPZ equation.

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BibTeXRIS

Jeremy Quastel, Alejandro Ramirez, Balint Virag. 2022-10-24. KPZ fluctuations in the planar stochastic heat equation. https://doi.org/10.1215/00127094-2024-0058

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