论文标题
在不断发展的随机环境中接触过程
Contact process in an evolving random environment
论文作者
论文摘要
在本文中，我们在具有有限程度的连接且具有有限程度的连接图表上，在不断发展的随机环境（CPERE）中介绍了一个接触过程，我们假设该环境是通过具有有限范围的Ergodic Spin Systems来描述的。我们表明，在一定的生长条件下，生存的相位转变与该过程的初始配置无关。我们研究了CPERE的不变定律，并表明在上述生长条件下，生存的相变与上层不变定律的非客气性的相变相吻合。此外，我们证明了生存概率的连续性特性，并以类似的方式与经典接触过程相似。然后，我们专注于特殊情况，在这种情况下，通过动态渗透来描述不断发展的随机环境。我们表明，在$ d $维整数上的动态渗透有关的联系过程死于A.S.在临界和完整的收敛范围内，所有参数选择都可以。最后，我们得出了具有有限范围的动力学渗透和具有有限范围的Ergodic旋转系统之间的一些比较结果，因此我们在不断发展的随机环境中获得接触过程的生存概率的界限，在这种情况下，我们确定完全收敛在某个参数方面中存在。
In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite range. We show that under a certain growth condition the phase transition of survival is independent of the initial configuration of the process. We study the invariant laws of the CPERE and show that under aforementioned growth condition the phase transition for survival coincides with the phase transition of non-triviality of the upper invariant law. Furthermore, we prove continuity properties for the survival probability and derive equivalent conditions for complete convergence, in an analogous way as for the classical contact process. We then focus on the special case, where the evolving random environment is described through a dynamical percolation. We show that the contact process on a dynamical percolation on the $d$-dimensional integer dies out a.s. at criticality and complete convergence holds for all parameter choices. In the end we derive some comparison results between a dynamical percolation and ergodic spin systems with finite range such that we get bounds on the survival probability of a contact process in an evolving random environment and we determine in this case that complete convergence holds in a certain parameter regime.
