Publications (4)
The shape theorem for the frog model
O. S. M. Alves, S. Yu. Popov, F. P. Machado
In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs), known as frog model. The dynamics of this process is described as follows: There are some act…
Extinction time in growth models subject to binomial catastrophes
F. Duque, V. V. Junior, F. P. Machado +1
Populations are often subject to catastrophes that cause mass removal of individuals. Many stochastic growth models have been considered to explain such dynamics. Among the results…
Phase transition for the frog model
O. S. M. Alves, F. P. Machado, S. Yu. Popov
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Eac…
The shape theorem for the frog model with random initial configuration
O. S. M. Alves, F. P. Machado, S. Yu. Popov +1
We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, whi…