发表机构
Universidade Estadual de Campinas (UNICAMP); Universidade Federal do ABC (UFABC)（坎皮纳斯州立大学; ABC联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有确定性治愈时间的广义接触过程，证明低感染率下灭绝、高感染率下存活，并给出单点密度性质。
AI 中文摘要
我们研究了一个在 \\(\mathbb{Z}^d\\) 上由感染率 \\(\lambda\\) 和重置概率 \\(p \in [0,1]\\) 参数化的广义接触过程，该过程模拟了确定性的治愈时间。一旦一个顶点被感染，其恢复被安排在一个时间单位之后。对已感染顶点的传入尝试以概率 \\(p\\) 成功重置其恢复时钟，否则被忽略。这统一了经典I型（\\(p=0\\)，非麻痹）和II型（\\(p=1\\)，麻痹）计数器的空间版本。除了完全重置的情况外，确定性的恢复截止时间破坏了坐标单调性并产生了因果屏蔽效应。利用对潜在因果链的一阶矩界，我们证明了当 \\(\lambda<1/(2d)\\) 时，过程从有限配置中灭绝，且该结果对 \\(p\in[0,1]\\) 一致成立。相同的因果链界还给出了从任意初始状态到空配置的局部收敛。在维度 \\(d \ge 2\\) 中，基于第一个感染窗口的有向渗流探索建立了当 \\(\lambda>-\log(1-p_c^{\mathrm{or}})\\) 时对所有 \\(p\in[0,1]\\) 的全局存活。最后，在纯非重置情形 \\(p=0\\) 下，我们推导了单点密度的延迟恒等式，并证明了该密度在任意有限时刻都严格介于0和1之间。
英文摘要
We study a generalized contact process on \(\mathbb{Z}^d\) parameterized by an infection rate \(λ\) and a resetting probability \(p \in [0,1]\), modeling deterministic cure times. Once a vertex is infected, its recovery is scheduled exactly one time unit later. Incoming attempts to an already-infected vertex successfully reset its recovery clock with probability \(p\), and are ignored otherwise. This unifies spatial versions of classical Type I (\(p=0\), non-paralyzable) and Type II (\(p=1\), paralyzable) counters. Except in the fully resetting case, deterministic recovery deadlines destroy coordinatewise attractiveness and create a causal shielding effect. Using a first-moment bound on potential causal chains, we prove that the process dies out from finite configurations whenever \(λ<1/(2d)\), uniformly in \(p\in[0,1]\). The same causal-chain bound yields local convergence to the empty configuration from arbitrary initial states. In dimensions \(d \ge 2\), an oriented percolation exploration based on the first infective window establishes global survival for all \(p\in[0,1]\) when \(λ>-\log(1-p_c^{\mathrm{or}})\). Finally, in the purely non-resetting case \(p=0\), we derive a delayed identity for the one-site density and prove that this density remains strictly between zero and one at every finite time.
Comments11 pages, 4 figures
