Pablo A. Gomes

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math.PR2026

Truncated long-range percolation of words on the square lattice

Pablo A. Gomes, OtÃ¡vio Lima, Roger W. C. Silva

We study mixed long-range percolation on the square lattice. Each vertical edge of unit length is independently open with probability $ε$ , and each horizontal edge of len…

math.PR2026

The extinction of the contact process in a one-dimensional random environment with long-range interactions

Pablo A. Gomes, Marcelo R. HilÃ¡rio, Bernardo N. B. de Lima +1

We study the contact process on the long-range percolation cluster on $Z$ where each edge $⟨ i, j ⟩$ is open with probability $∣ i - j ∣^{- s}$ for $s > 2$ . Using a r…

math.PR2026

Upper bounds for critical probabilities in Bernoulli Percolation models

Pablo A. Gomes, Alan Pereira, Remy Sanchis

We consider bond and site Bernoulli Percolation in both the oriented and the non-oriented cases on $Z^{d}$ and obtain rigorous upper bounds for the critical points in those…