Author

Denis A. Luiz

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Preprint Aug 2026

Extinction, Survival and Fluctuations for the Spatial Maki--Thompson Model on Infinite Graphs

We study the spatial Maki--Thompson rumor model on infinite, connected graphs of bounded degree. Spreaders transmit the rumor to ignorant neighbors but become stiflers upon contacting non-ignorant neighbors. We prove extinction on Cayley graphs of linear growth, for every \(\lambda,\alpha>0\) and every initial configur...

L. H. D. de Araújo, D. M. Machado, Cristian F. Coletti et al. · 0 citations

Preprint Sep 2026

Extinction and Survival for a Generalized Contact Process with Deterministic Cures

We study a generalized contact process on \(\mathbb{Z}^d\) parameterized by an infection rate \(\lambda\) and a resetting probability \(p \in [0,1]\), modeling deterministic cure times. Once a vertex is infected, its recovery is scheduled exactly one time unit later. Incoming attempts to an already-infected vertex succ...

Nancy L. Garcia, Denis A. Luiz, D. M. Machado · 0 citations