论文标题
非生存的概率证明：Galton-Watson过程等等
Probabilistic proof for non-survival at criticality: The Galton-Watson process and more
论文作者
论文摘要
Bezuidenhout和Grimmett在著名的论文中证明了接触过程在关键点消失了。它们的证明技术通常用于研究人口模式的增长。本文的目的是对他们的想法的介绍，并以最少的技术性为例。特别是，我们恢复了有关加尔顿 - 沃特森链的基本定理：除了在退化的情况下，只有在生育率超过1的情况下才有可能生存。在课堂上教授的经典证据基本上是基于产生功能和凸性参数的分析性的。按照Bezuidenhout-Grimmett方式，我们提出了一个与概率直觉更一致的证明。我们还研究了原始模型的生存问题，混合了性和无性繁殖。
In a famous paper, Bezuidenhout and Grimmett demonstrated that the contact process dies out at the critical point.Their proof technique has often been used to study the growth of population patterns. The present text is intended as an introduction to their ideas, with examples of minimal technicality. In particular, we recover the basic theorem about Galton-Watson chains: except in a degenerate case, survival is possible only if the fertility rate exceeds 1. The classical proof that is taught in classrooms is essentially analytic, based on generating functions and convexity arguments. Following the Bezuidenhout-Grimmett way, we propose a proof that is more consistent with probabilistic intuition. We also study the survival problem for an original model, mixing sexual and asexual reproduction.
