A PHASE-TRANSITION FOR A STOCHASTIC PDE RELATED TO THE CONTACT PROCESS
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 0178-8051Full text not available from this repository.
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|
|Number of Pages:||26|
|Page Range:||pp. 131-156|
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