Stochastic heat flow is a black noise

TL;DR

This paper proves that the stochastic heat flow is a black noise, implying asymptotic independence from the driving noise in the 2D stochastic heat equation under certain scaling limits.

Contribution

It establishes that the stochastic heat flow qualifies as a black noise, advancing understanding of its independence properties in the scaling limit.

Findings

Stochastic heat flow is classified as a black noise.

The 2D stochastic heat equation becomes asymptotically independent of mollified noise.

Provides a rigorous proof connecting stochastic heat flow to Tsirelson's black noise concept.

Abstract

We prove that the stochastic heat flow Caravenna Sun Zygouras (2023), Tsai (2024) is a black noise in the sense of Tsirelson (2004). As a corollary, the 2d stochastic heat equation driven by a mollified spacetime white noise becomes asymptotically independent of that noise in the scaling limit.