论文标题
与几何寿命的同质树上的青蛙模型的关键参数
Critical parameter of the frog model on homogeneous trees with geometric lifetime
论文作者
论文摘要
我们考虑尺寸$ d $的同质树上的几何寿命（参数$ 1-p $）的青蛙模型。在2002年，\ cite {alves2002-2}证明，存在一个关键的寿命参数$ p_c \ in（0,1）$，而无限的许多青蛙则以正概率激活，并且它们以$ p_c $的价格给出了下界和上限。从那时起，有关该模型的文献集中在上限的改进上。在本文中，我们改善了$ p_c $ \ emph {双方}的界限。我们还提供了比较文献及其证明的界限的讨论。我们的证明是基于耦合的。
We consider the frog model with geometric lifetime (parameter $1-p$) on homogeneous trees of dimension $d$. In 2002, \cite{alves2002-2} proved that there exists a critical lifetime parameter $p_c\in(0,1)$ above which infinitely many frogs are activated with positive probability, and they gave lower and upper bounds for $p_c$. Since then, the literature on this model focussed on refinements of the upper bound. In the present paper we improve the bounds for $p_c$ \emph{on both sides}. We also provide a discussion comparing the bounds of the literature and their proofs. Our proofs are based on coupling.
