Gaussian Fields and Stochastic Heat Equations
Sergey Lototsky, Apoorva Shah
TL;DR
This paper characterizes Gaussian free fields as stationary solutions to stochastic heat equations driven by white noise, revealing new types of Gaussian fields and phenomena in low dimensions.
Contribution
It provides a novel characterization of Gaussian free fields via stochastic heat equations and explores their properties across different spatial dimensions.
Findings
Gaussian free fields can be realized as stationary solutions to stochastic heat equations.
Different types of Gaussian fields emerge in the whole space setting.
Unique phenomena occur in dimensions one and two.
Abstract
The objective of the paper is to characterize the Gaussian free field as a stationary solution of the heat equation with additive space-time white noise. In the case of whole space, the investigation leads to other types of Gaussian fields, as well as interesting phenomena in dimensions one and two.
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Taxonomy
TopicsStochastic processes and financial applications · Advanced Thermodynamics and Statistical Mechanics · Statistical Mechanics and Entropy