### Abstract

We consider a jump-diffusion process describing a system of diffusing particles that upon contact with an obstacle (catalyst) die and are replaced by an independent offspring with position chosen according to a weighted average of the remaining particles. The obstacle is a bounded nonnegative function V (x) and the birth/death mechanism is similar to the Fleming-Viot critical branching. Since the mass is conserved, we prove a hydrodynamic limit for the empirical measure, identified as the solution to a generalized semilinear (reaction-diffusion) equation, with nonlinearity given by a quadratic operator. A large-deviation principle from the deterministic hydrodynamic limit is provided. The upper bound is given in any dimension, and the lower bound is proven for d = 1 and V bounded away from 0. An explicit formula for the rate function is provided via an Orlicz-type space.

Original language | English (US) |
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Pages (from-to) | 1056-1080 |

Number of pages | 25 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 60 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2007 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics