TY - JOUR

T1 - Quenched asymptotics for survival probabilities in the random saturation process

AU - Ben Arous, Gérard

AU - Ramírez, Alejandro F.

N1 - Funding Information:
where Cd := 3d2 2d-1 Acknowledgement. The first author thanks Michel Renard and Science & Tee for the initial motivation for this project. The second author acknowledges partial financial support by Fondo National de Desarrollo Cientifico y Tecnologico. Both authors thank Ostap Hryniv, Jeremy Quastel and Vladas Sidoravicius for helpful comments.

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].

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U2 - 10.1016/S0764-4442(00)88627-9

DO - 10.1016/S0764-4442(00)88627-9

M3 - Article

AN - SCOPUS:0033426915

SN - 0764-4442

VL - 329

SP - 1003

EP - 1008

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

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

IS - 11

ER -