From disordered systems to the Critical 2D Stochastic Heat Flow

Francesco Caravenna; Rongfeng Sun; Nikos Zygouras

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arXiv · 2511.08479

From disordered systems to the Critical 2D Stochastic Heat Flow

Francesco Caravenna·Rongfeng Sun·Nikos Zygouras

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Abstract

We review our joint work on the scaling limits of disordered systems, linking the notion of disorder relevance/irrelevance to that of sub/super-criticality of singular SPDEs. This line of research culminated in the construction of the Critical 2D Stochastic Heat Flow (SHF), a universal process which provides a non-trivial solution to the Stochastic Heat Equation in dimension 2, a critical singular SPDE that lies beyond the reach of existing solution theories. The SHF also offers a rare example of a non-Gaussian scaling limit for a disordered system at its phase transition point in the critical dimension.

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BibTeX RIS

Francesco Caravenna, Rongfeng Sun, Nikos Zygouras. 2025-11-11. From disordered systems to the Critical 2D Stochastic Heat Flow. https://arxiv.org/abs/2511.08479

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