The critical 2d stochastic heat flow (SHF) is a stochastic process of random measures on ℝ2, recently constructed in (Invent. Math. 233 (2023) 325–460).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.
Caravenna, F., Sun, R., Zygouras, N. (2023). The critical 2d stochastic heat flow is not a Gaussian multiplicative chaos. ANNALS OF PROBABILITY, 51(6), 2265-2300 [10.1214/23-aop1648].
The critical 2d stochastic heat flow is not a Gaussian multiplicative chaos
Caravenna, F;
2023
Abstract
The critical 2d stochastic heat flow (SHF) is a stochastic process of random measures on ℝ2, recently constructed in (Invent. Math. 233 (2023) 325–460).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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