The disk-percolation model on graphs

Rumor Processes on N

“…The focus used to be on deterministic or stochastic models, modeling homogeneously mixed populations living on spaces with no structure, as in the Maki-Thompson (see [15] and [18]) and Daley-Kendall (see [5] and [17]) models. Possible variations that can be found in the recent literature include competing rumors (see [11]), more than two people meeting at a time (see [10]), moving agents (see [12]) and rumors through tree-like graphs (see [13] and [14]), complex networks (see [9]), grids (see [1]), and multigraphs (see [2]). …”

The Rumor Percolation Model and Its Variations

“…Theorem 3.1 (Lebenstayn and Rodriguez [12]). Let G be of bounded degree (∆ < ∞) and be such that p site c (G) < 1.…”

“…They work with the concept of the coverage of a set (t, ∞) d for some t > 0, the eventual coverage. In section 3 we review the paper of Lebenstayn and Rodriguez [12] where authors consider the Disk Percolation Model. While the set of radius of influence, {R v } {v∈V} , has a geometric distribution, the graph G is quite general.…”

Modelagem de epidemias via sistemas de partículas interagentes

“…Considere um Processo Firework Contínuo sobre os inteiros não-negativos com alcances (2). Pelo Corolário 3.2.1.1, P(V ) = 0.…”

“…Em [2], os autores encontram condições de sobrevivência para o caso onde os alcances têm distribuição geométrica. Logo, para todo n ≥ 1 fixado, (Z n j ) j≥0é um processo de ramificação cuja sobrevivência implica na sobrevivência do processo Firework Discreto.…”