Volume 25, 2021
|Page(s)||204 - 219|
|Published online||23 March 2021|
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Av. dos Estados, 5001,
São Paulo, Brazil.
*** Corresponding author: email@example.com
Accepted: 26 January 2021
We study the frog model on Cayley graphs of groups with polynomial growth rate D ≥ 3. The frog model is an interacting particle system in discrete time. We consider that the process begins with a particle at each vertex of the graph and only one of these particles is active when the process begins. Each activated particle performs a simple random walk in discrete time activating the inactive particles in the visited vertices. We prove that the activation time of particles grows at least linearly and we show that in the abelian case with any finite generator set the set of activated sites has a limiting shape.
Mathematics Subject Classification: 60K35 / 60D05 / 52A22 / 60F15 / 60J10
Key words: Shape theorem / frog model / Cayley graph / interacting particle system
© EDP Sciences, SMAI 2021
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