Coexistence of lazy frogs on ℤ

Abstract

We study the so-called frog model on with two types of lazy frogs, with parameters respectively, and a finite expected number of dormant frogs per site. We show that for any such and 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.