The initial set in the frog model is irrelevant

2019/12/20 by Maria Deijfen, Deijfen, Maria, Sebastian Rosengren +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1912.10085

arxiv created 2019/12/20 · arxiv updated 2019/12/24

Abstract

In this note, we consider the frog model on ℤ^d and a two-type version of it with two types of particles. For the one-type model, we show that the asymptotic shape does not depend on the initially activated set and the configuration there. For the two-type model, we show that the possibility for the types to coexist in that both of them activate infinitely many particles does not depend on the choice of the initially activated sets and the configurations there.

Related

• Competing frogs on ℤ^d
• The shape theorem for the frog model with random initial configuration
• The nonhomogeneous frog model on ℤ
• The shape theorem for the frog model
• Frog model on ℤ with random survival parameter