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arXiv · 2206.08766

The critical 2d Stochastic Heat Flow is not a Gaussian Multiplicative Chaos

Francesco Caravenna·Rongfeng Sun·Nikos Zygouras
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Abstract

The critical $2d$ Stochastic Heat Flow (SHF) is a stochastic process of random measures on ${\mathbb R}^2$, recently constructed in [CSZ23]. We show that this process falls outside the class of Gaussian Multiplicative Chaos (GMC), in the sense that it cannot be realised as the exponential of a (generalised) Gaussian field. We achieve this by deriving strict lower bounds on the moments of the SHF that are of independent interest.

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Francesco Caravenna, Rongfeng Sun, Nikos Zygouras. 2022-06-17. The critical 2d Stochastic Heat Flow is not a Gaussian Multiplicative Chaos. https://doi.org/10.1214/23-aop1648

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