Finite Width For a Random Stationary Interface

Carl Mueller (University of Rochester)
Roger Tribe (University of Warwick)

Abstract


We study the asymptotic shape of the solution $u(t,x) \in [0,1]$ to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is $u(0,x)$ is 0 for all large positive $x$ and $u(0,x)$ is 1 for all large negitive $x$. The special form of the noise term preserves this property at all times $t \geq 0$. The main result is that, in contrast to the deterministic heat equation, the width of the interface remains stochastically bounded.

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Pages: 1-27

Publication Date: October 16, 1997

DOI: 10.1214/EJP.v2-21

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