Author

Gustavo O. De Carvalho

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Preprint Sep 2026

Phase transitions for percolation of words in one dimension

In this paper, we investigate models of percolation of words on $\mathbb{Z}_+$ with long-range connections. The underlying graph is oriented and constructed according to a sequence of non-negative ranges. In the first model, the sequence of ranges is considered random and, in the second model, deterministic and non-dec...

Gustavo O. De Carvalho, P. A. Gomes · 0 citations

Preprint Jul 2026

Extinction and Survival in an Interval-Activation Frog Model on \mathbb{Z} with Random Survival Parameters and Symmetric Random Walks

We study an interval-activation frog model on $\mathbb Z$ with i.i.d.\ initial numbers of frogs $(\eta_x)_{x\in\mathbb Z}$, satisfying $0<\mathbb{E}[\eta_0]<\infty$. Frogs at the origin are initially active and all others are sleeping. Each frog performs a symmetric integer-valued random walk and has a random lif...

Gustavo O. De Carvalho, F. P. Machado, J. H. Ramírez-González · 0 citations