标题： 一般接触过程：非均匀模型、图上的模型和流形上的模型 显示英文标题

标题： General contact processes: inhomogeneous models, models on graphs and on manifolds

摘要： 接触过程是无限粒子配置上的生灭过程的一个特例。 我们考虑在局部紧致可分度量空间上的接触模型。 我们在对关联的马尔可夫跳跃过程施加条件的情况下，证明了临界区域中存在一个单参数的不变测度集合。 这个条件大致要求该跳跃过程的任何一对轨迹之间的分离。 该一般方案可以应用于具有异质和随机环境的格点上的接触过程，以及图和流形上的接触过程。 显示英文摘要

摘要： The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant measures in the critical regime under the condition imposed on the associated Markov jump process. This condition, roughly speaking, requires the separation of any pair of trajectories of this jump process. The general scheme can be applied to the contact process on the lattice in a heterogeneous and random environments as well as to the contact process on graphs and on manifolds.