Competing frogs on \({\mathbb Z}^d\)

DOI10.1214/19-EJP400zbMath1428.60137arXiv1902.01849WikidataQ122891235 ScholiaQ122891235MaRDI QIDQ2285792

Maria Deijfen, Timo Hirscher, Fabio Lopes

Publication date: 9 January 2020

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.01849

zbMATH Keywords

frog modelrandom walkcoexistencecompeting growth

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (8)

Competition on \(\mathbb{Z}^d\) driven by branching random walk ⋮ A stochastic combustion model with thresholds on trees ⋮ Explosion and non-explosion for the continuous-time frog model ⋮ The initial set in the frog model is irrelevant ⋮ The continuous-time frog model can spread arbitrarily fast ⋮ On transience of frogs on Galton-Watson trees ⋮ Coexistence in discrete time multi-type competing frog models ⋮ Coexistence of lazy frogs on

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• From transience to recurrence with Poisson tree frogs
• First-passage competition with different speeds: positive density for both species is impossible
• An improved subadditive ergodic theorem
• Ergodic theorems for the multitype contact process
• Recurrence and transience for the frog model on trees
• Branching random walk with catalysts
• On infection spreading and competition between independent random walks
• Coexistence for Richardson type competing spatial growth models
• Coexistence in two-type first-passage percolation models
• Phase transition for the frog model
• The shape theorem for the frog model
• Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model.
• Asymptotic behavior of a stochastic combustion growth process
• The asymmetric multitype contact process
• Multi-particle diffusion limited aggregation
• The spread of a rumor or infection in a moving population
• A shape theorem for the spread of an infection
• The Pleasures and Pains of Studying the Two-Type Richardson Model
• First passage percolation and a model for competing spatial growth
• Moderate Deviations for I.I.D. Random Variables
• Competition in growth and urns
• Coexistence in a two-type continuum growth model
• A stochastic model for competing growth on $\mathbb{R}^d$
• Branching and tree indexed random walks on fractals
• Functional central limit theorem for the interface of the multitype contact process

This page was built for publication: Competing frogs on \({\mathbb Z}^d\)