Frogs on trees?

J Hermon - 2018‏ - projecteuclid.org
We study a system of simple random walks on T_d,n=(\calV_d,n,\calE_d,n), the d-ary tree of
depth n, known as the frog model. Initially there are Pois (λ) particles at each site …

Frogs and some other interacting random walks models

SY Popov - Discrete Mathematics & Theoretical Computer …, 2003‏ - dmtcs.episciences.org
We review some recent results for a system of simple random walks on graphs, known
as\emphfrog model. Also, we discuss several modifications of this model, and present a few …

Linear and superlinear spread for stochastic combustion growth process

V Bezborodov, T Krueger - Annales de l'Institut Henri Poincare (B) …, 2024‏ - projecteuclid.org
Consider a stochastic growth model on Z d. Start with some active particle at the origin and
slee** particles elsewhere. The initial number of particles at x∈ Z d is η (x), where (η (x)) …

Cover time for the frog model on trees

C Hoffman, T Johnson, M Junge - Forum of Mathematics, Sigma, 2019‏ - cambridge.org
COVER TIME FOR THE FROG MODEL ON TREES Page 1 Forum of Mathematics, Sigma (2019),
Vol. 7, e41, 49 pages doi:10.1017/fms.2019.37 1 COVER TIME FOR THE FROG MODEL ON …

The coverage ratio of the frog model on complete graphs

GO de Carvalho, FP Machado - Journal of Statistical Physics, 2023‏ - Springer
The frog model is a system of interacting random walks. Initially, there is one particle at each
vertex of a connected graph. All particles are inactive at time zero, except for the one which …

Laws of large numbers for the frog model on the complete graph

E Lebensztayn, MA Estrada - Journal of Mathematical Physics, 2019‏ - pubs.aip.org
The frog model is a stochastic model for the spreading of an epidemic on a graph in which a
dormant particle starts to perform a simple random walk on the graph and to awaken other …

Critical Conditions for the Coverage of Complete Graphs with the Frog Model

GO de Carvalho, FP Machado - arxiv preprint arxiv:2407.19027, 2024‏ - arxiv.org
We consider a system of interacting random walks known as the frog model. Let $\mathcal
{K} _n=(\mathcal {V} _n,\mathcal {E} _n) $ be the complete graph with $ n $ vertices and …

Brownian snails with removal: epidemics in diffusing populations

GR Grimmett, Z Li - Electronic Journal of Probability, 2022‏ - projecteuclid.org
Two stochastic models of susceptible/infected/removed (SIR) type are introduced for the
spread of infection through a spatially-distributed population. Individuals are initially …

The social network model on infinite graphs

J Hermon, B Morris, C Qin, A Sly - The Annals of Applied Probability, 2020‏ - JSTOR
Given an infinite connected regular graph G=(V, E), place at each vertex Poisson (λ) walkers
performing independent lazy simple random walks on G simultaneously. When two walkers …

The end time of SIS epidemics driven by random walks on edge-transitive graphs

D Figueiredo, G Iacobelli, S Shneer - Journal of Statistical Physics, 2020‏ - Springer
Network epidemics is a ubiquitous model that can represent different phenomena and finds
applications in various domains. Among its various characteristics, a fundamental question …