Gaussian fluctuations for the stochastic Burgers equation in dimension \(d \geq 2\)
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Publication:6203021
DOI10.1007/S00220-024-04966-ZarXiv2304.05730OpenAlexW4392961657MaRDI QIDQ6203021
Author name not available (Why is that?)
Publication date: 26 March 2024
Published in: (Search for Journal in Brave)
Abstract: The goal of the present paper is to establish a framework which allows to rigorously determine the large-scale Gaussian fluctuations for a class of singular SPDEs at and above criticality, and therefore beyond the range of applicability of pathwise techniques, such as the theory of Regularity Structures. To this purpose, we focus on a -dimensional generalization of the Stochastic Burgers equation (SBE) introduced in [H. van Beijeren, R. Kutner and H. Spohn, Excess noise for driven diffusive systems, PRL, 1985]. In both the critical and super-critical cases, we show that the scaling limit of (the regularised) SBE is given by a stochastic heat equation with non-trivially renormalised coefficient, introducing a set of tools that we expect to be applicable more widely. For the scaling adopted is the classical diffusive one, while in it is the weak coupling scaling which corresponds to tuning down the strength of the interaction in a scale-dependent way.
Full work available at URL: https://arxiv.org/abs/2304.05730
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