Approximations finies de la mesure invariante du processus de contact sur-critique vu par la première particule. (Finite approximations of the invariant measure of supercritical contact processes as seen from the first particle) (Q1113222)

For each integer \(n\geq 1\) we consider the contact process as seen from the first particle and we do not allow the process to disappear or to have more than n particles. We prove that the invariant probability of this process converges to a limit when n goes to infinity. This limit is exactly the invariant probability measure of the usual contact process as seen from the first particle. \textit{R. Durrett} [Ann. Probab. 12, 999-1040 (1984; Zbl 0567.60095)] has proven the existence of this probability and the first author and \textit{E. Presutti} [ibid. 15, 1131-1145 (1987; Zbl 0645.60103)] have shown its uniqueness. We obtain here a new proof of the existence of this probability and a complete convergence theorem for finite and infinite initial configurations.