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A phase transition for a stochastic PDE related to the contact process (1994)

Mueller, Carl ; Tribe, Roger

Springer

Probability theory and related fields 100 (1994), S. 131-156

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ISSN: 1432-2064

Keywords: 60H15 ; 35R60

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary 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 longrange 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01199262

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