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A PHASE-TRANSITION FOR A STOCHASTIC PDE RELATED TO THE CONTACT PROCESS
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UNSPECIFIED (1994) A PHASE-TRANSITION FOR A STOCHASTIC PDE RELATED TO THE CONTACT PROCESS. PROBABILITY THEORY AND RELATED FIELDS, 100 (2). pp. 131-156. ISSN 0178-8051
Full text not available from this repository.Abstract
We consider the one-dimensional heat equation, with a semilinear term and with a nonlinear white noise term. R. Durrett conjectured that this equation arises as a weak limit of the contact process with long-range interactions. We show that our equation possesses a phase transition. To be more precise, we assume that the initial function is nonnegative with bounded total mass. If a certain parameter in the equation is small enough, then the solution dies out to 0 in finite time, with probability 1. If this parameter is large enough, then the solution has a positive probability of never dying out to 0. This result answers a question of Durett.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Journal or Publication Title: | PROBABILITY THEORY AND RELATED FIELDS |
| Publisher: | SPRINGER VERLAG |
| ISSN: | 0178-8051 |
| Date: | October 1994 |
| Volume: | 100 |
| Number: | 2 |
| Number of Pages: | 26 |
| Page Range: | pp. 131-156 |
| Publication Status: | Published |
| URI: | http://wrap.warwick.ac.uk/id/eprint/20233 |
Data sourced from Thomson Reuters' Web of Knowledge
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