Abstract:We study the one-dimensional modified boundary contact process, in which infections across the two boundary edges of the infected region occur at rate $\lambda_e$, while all other infections occur at rate $\lambda_i$. We prove two results in different parts of the phase diagram. First, in the non-attractive region $\lambda_e>\lambda_i\geq\lambda_c$, where $\lambda_c$ is the critical parameter of the standard contact process, the process seen from its rightmost infected site converges from every semi-infinite initial configuration to an invariant measure. Second, on the critical curve in the attractive region, the infection dies out almost surely.
From: Célio Terra [view email]
[v1]
Wed, 12 Mar 2025 18:22:54 UTC (59 KB)
[v2]
Thu, 30 Jul 2026 17:35:00 UTC (60 KB)
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