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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Pages: 293-315

Publication Date: April 9, 2004

DOI: 10.1214/EJP.v9-197

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