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 Electronic Journal of Probability > Vol. 2 (1997) > Paper 7 open journal systems 


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.


Full text: PDF

Pages: 1-27

Published on: October 16, 1997
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Electronic Journal of Probability. ISSN: 1083-6489