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Finite Width For a Random Stationary Interface


 
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1. Title Title of document Finite Width For a Random Stationary Interface
 
2. Creator Author's name, affiliation, country Carl Mueller; University of Rochester
 
2. Creator Author's name, affiliation, country Roger Tribe; University of Warwick
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Stochastic partial differential equations, duality, travelling waves, white noise
 
3. Subject Subject classification Primary 60H15; secondary 35R60
 
4. Description 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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7. Date (YYYY-MM-DD) 1997-10-16
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/21
 
10. Identifier Digital Object Identifier 10.1214/EJP.v2-21
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 2
 
12. Language English=en en
 
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