Critical Parameter of the Frog Model on Homogeneous Trees with Geometric Lifetime
نویسندگان
چکیده
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 parameter $p_c\in(0,1)$ above which infinitely many frogs are activated positive probability, and they gave lower upper bounds for $p_c$. Since then, literature this focussed refinements bound. present paper we improve $p_c$ \emph{on both sides}. also provide discussion comparing their proofs. Our proofs based coupling.
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2022
ISSN: ['0022-4715', '1572-9613']
DOI: https://doi.org/10.1007/s10955-022-03049-4