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Moments of the 2D SHE at criticality
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abstract
We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as the limit of the equation driven by a noise that is mollified in space and white in time. As the mollification radius $ \varepsilon\to 0 $, we tune the coupling constant near the critical point, and show that the single time correlation functions converge to a limit written in terms of an explicit non-trivial semigroup. Our approach consists of two steps. First we show the convergence of the resolvent of the (tuned) two-dimensional delta Bose gas, by adapting the framework of Dimock and Rajeev (2004) to our setup of spatial mollification. Then we match this to the Laplace transform of our semigroup.
Forward citations
Cited by 3 Pith papers
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The conditional Gaussian multiplicative chaos structure underlying a critical continuum random polymer model on a diamond fractal
The critical continuum polymer measures on the dimension-two diamond fractal are shown to satisfy a conditional Gaussian multiplicative chaos relation: M_{r+a} equals in law a subcritical GMC over M_r.
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Continuum models of directed polymers on disordered diamond fractals in the critical case
Critical continuum random polymer measures M_r are constructed on diamond fractals, and intersections of two independent paths are shown to have Hausdorff dimension zero with log-Hausdorff exponent 1.
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Weak-disorder limit at criticality for directed polymers on hierarchical graphs
The partition functions for directed polymers on diamond graphs with b=s converge in distribution to a unique limit law under a fine-tuned critical inverse-temperature scaling.
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