On Infection Spreading and Competition between Independent Random Walks
Irina Kurkova, Université de Paris VI (Pierre et Marie Curie), France
Serguei Popov, Universidade de São Paulo, Brasil
M. Vachkovskaia, Universidade de Campinas, Brasil
Abstract
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.).
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