A New Upper Bound for the Critical Probability of the Frog Model on Homogeneous Trees

Autor(es)

Lebensztayn, Elcio ^[1] ; Utria, Jaime ^[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] Fluminense Fed Univ UFF, Inst Math & Stat, Rua Prof Marcos Waldemar Freitas Reis S-N, BR-24210201 Niteroi, RJ - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 176, n. 1, p. 169-179, JUL 2019.
• Citações Web of Science: 1

Resumo

We consider the interacting particle system on the homogeneous tree of degree (d+1), known as frog model. In this model, active particles perform independent random walks, awakening all sleeping particles they encounter, and dying after a random number of jumps, with geometric distribution. We prove an upper bound for the critical parameter of survival of the model, which improves the previously known results. This upper bound was conjectured in a paper by Lebensztayn et al. (J Stat Phys 119(1-2):331-345, 2005). We also give a closed formula for the upper bound. (AU)

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