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KPZ fluctuations in the planar stochastic heat equation

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arxiv 2210.13607 v3 pith:QLUNZXHY submitted 2022-10-24 math.PR math-phmath.APmath.MP

Jeremy Quastel , Alejandro Ramirez , Balint Virag This is my paper · ORCID
classification math.PRmath-phmath.APmath.MP
keywords equationfluctuationsgivenheatplanarstochasticcentrechaos
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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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  1. Conditional GMC within the stochastic heat flow

    math.PR 2025-07 conditional novelty 8.0 of 10

    The family of polymer measures of the critical 2D stochastic heat flow has a conditional GMC structure: a GMC with noise strength a maps M^theta in law to M^(theta+a).

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