The asymptotic shape theorem for the frog model on finitely generated abelian groups
| Autor: | Cristian F. Coletti, Lucas R. de Lima |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
60K35 60D05 52A22 60F15 60J10 Polynomial Interacting particle system Cayley graph Probability (math.PR) 010102 general mathematics 01 natural sciences Vertex (geometry) Combinatorics 010104 statistics & probability Discrete time and continuous time FOS: Mathematics Graph (abstract data type) 0101 mathematics Abelian group Mathematics - Probability Mathematics Generator (mathematics) |
| Popis: | We study the frog model on Cayley graphs of groups with polynomial growth rate $D \geq 3$. 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. The original publication is available at www.esaim-ps.org |
| Databáze: | OpenAIRE |
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