Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60K35 Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
- 82C22 Interacting particle systems [See also 60K35]

**Résumé:** We study the models of competition and spreading of infection for infinite
systems
of independent random walks. For the competition model, we investigate the
question
whether one of the spins prevails with probability one. For the infection
spreading, we give sufficient conditions for recurrence and transience
(i.e., whether the origin will be visited by infected particles infinitely
often a.s.).

**Mots Clés:** *simple random walk ; transience ; recurrence*

**Date:** 2003-11-20

**Prépublication numéro:** *PMA-866*