the lower critical magnetic field

When this branching processes in random environments is subcritical, it is a certainty that its two copying processes can be migrated a supercritical branching processes in random environments through giving an acute probability generating function derivative.

给定一个繁衍概率母函数均值待定的两状态独立同分布随机环境分枝过程,证明了若该随机环境分枝过程是下临界的,则通过适当选择其繁衍概率母函数均值的取值后,它的两个独立复制过程总能够混合重组为一个上临界随机环境分枝过程;但反之,若该随机环境分枝过程是上临界的,则它的两个独立复制过程不一定总能够混合重组为一个下临界随机环境分枝过程。

We study the general model of branching processes in random environment and discuss their properties,moreover,we introduce the concepts of general subcritical branching chain in random environment and get their properties.

研究了随机环境中分枝链的一般模型,并讨论了它们的一些性质,在此基础引入广义的下临界分支链的概念并得到了相应的性质。