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

Autor(es)

Lebensztayn, Elcio ^[1] ; Estrada, Mario Andres ^[2]

Afiliação do(s) autor(es)

^[1] Univ Campinas UNICAMP, Inst Math Stat & Sci Computat, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Fed Univ Pernambuco UFPE, Dept Stat, Ave Prof Luiz Freire S-N, BR-50740540 Recife, PE - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 60, n. 12 DEC 1 2019.
• Citações Web of Science: 0

Resumo

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 particles once it becomes active. We study two versions of the frog model on the complete graph with N + 1 vertices. In the first version that we consider, active particles have geometrically distributed lifetimes. In the second version, the displacement of each awakened particle lasts until it hits a vertex already visited by the process. For each model, we prove that as N -> infinity, the trajectory of the process is well approximated by a three-dimensional discrete-time dynamical system. We also study the long-term behavior of the corresponding deterministic systems. (AU)

• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático