### Abstract

We report on the recent work [3]. There, the asymptotics of the survival probabilities of particles in a random environment of obstacles, are computed. The model is the following: particles are injected at a time dependent rate at the origin of the lattice ℤ^{d}. Once born, they diffuse among sites which are free of traps. Each trap has a random depth, which decreases by one each time a particle is absorbed. The logarithmic asymptotic decay of the probability that a particle born at some fixed time survives at some later time t is computed, showing the presence of three injection regimes. Here we report on the quenched version of these results. A key tool for proving this result is the method of enlargement of obstacles developed by Sznitman [9].

Translated title of the contribution | Quenched asymptotics for survival probabilities in the random saturation process |
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Original language | French |

Pages (from-to) | 1003-1008 |

Number of pages | 6 |

Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |

Volume | 329 |

Issue number | 11 |

DOIs | |

State | Published - Dec 1 1999 |

### ASJC Scopus subject areas

- Mathematics(all)