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Fluctuations of a nonlinear stochastic heat equation in dimensions three and higher
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Fluctuations of a nonlinear stochastic heat equation in dimensions three and higher
classification
math.PR
keywords
equationfluctuationsheatnonlinearsolutionstochastictimeconstant
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We study the solution to a nonlinear stochastic heat equation in $d\geq 3$. The equation is driven by a Gaussian multiplicative noise that is white in time and smooth in space. For a small coupling constant, we prove (i) the solution converges to the stationary distribution in large time; (ii) the diffusive scale fluctuations are described by the Edwards-Wilkinson equation.
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