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Coexistence of lazy frogs on
${\mathbb{Z}}$
Published online by Cambridge University Press: 28 June 2022
Abstract
We study the so-called frog model on
${\mathbb{Z}}$
with two types of lazy frogs, with parameters
$p_1,p_2\in (0,1]$
respectively, and a finite expected number of dormant frogs per site. We show that for any such
$p_1$
and
$p_2$
there is positive probability that the two types coexist (i.e. that both types activate infinitely many frogs). This answers a question of Deijfen, Hirscher, and Lopes in dimension one.
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- Original Article
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust
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