Tzioufas, Achillefs The entirely coupled region of supercritical contact processes. (English) Zbl 1351.60131 J. Appl. Probab. 53, No. 3, 925-929 (2016). Summary: We consider translation-invariant, finite-range, supercritical contact processes. We show the existence of unbounded space-time cones within which the descendancy of the process from full occupancy may with positive probability be identical to that of the process from the single site at its apex. The proof comprises an argument that leans upon refinements of a successful coupling among these two processes, and is valid in \(d\)-dimensions. MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C43 Time-dependent percolation in statistical mechanics Keywords:contact processes; asymptotic shape theorem; coupling; finite range; coupling event; coupling time × Cite Format Result Cite Review PDF Full Text: DOI arXiv