@article{EJP21,
author = {Carl Mueller and Roger Tribe},
title = {Finite Width For a Random Stationary Interface},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {2},
year = {1997},
keywords = {Stochastic partial differential equations, duality, travelling waves, white noise},
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.},
pages = {no. 7, 1-27},
issn = {1083-6489},
doi = {10.1214/EJP.v2-21},
url = {http://ejp.ejpecp.org/article/view/21}}