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Gaussian Fields and Stochastic Heat Equations (2008.00056v1)
Published 31 Jul 2020 in math.PR
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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