The critical contact process seen from the right edge
\textit{R. Durrett} [Ann. Probab. 12, 999-1040 (1984; Zbl 0567.60095)] proved the existence of an invariant measure for the critical and supercritical contact process seen from the right edge. \textit{A. Galves} and \textit{E. Presutti} [ibid. 15, 1131-1145 (1987; Zbl 0645.60103)] proved, in the supercritical case, that the invariant measure was unique, and convergence to it held starting in any semi-infinite initial state. We prove the same for the critical contact process. We also prove that the process starting with one particle, conditioned to survive until time t, converges to the unique invariant measure as \(t\to \infty\).
scientific article; zbMATH DE number 4137168