### 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].

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 |

State | Published - Dec 1 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Comptes Rendus de l'Academie des Sciences - Series I: Mathematics*,

*329*(11), 1003-1008.

**Asymptotiques presque sûres des probabilités de survie dans le processus de saturation aléatoire.** / Ben Arous, Gérard; Ramírez, Alejandro F.

Research output: Contribution to journal › Article

*Comptes Rendus de l'Academie des Sciences - Series I: Mathematics*, vol. 329, no. 11, pp. 1003-1008.

}

TY - JOUR

T1 - Asymptotiques presque sûres des probabilités de survie dans le processus de saturation aléatoire

AU - Ben Arous, Gérard

AU - Ramírez, Alejandro F.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - 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 ℤd. 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].

AB - 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 ℤd. 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].

UR - http://www.scopus.com/inward/record.url?scp=0033426915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033426915&partnerID=8YFLogxK

M3 - Article

VL - 329

SP - 1003

EP - 1008

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 11

ER -