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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