Pablo Almeida Gomes

University of São Paulo | USP · Department of Statistics (IME) (São Paulo)

We establish central limit theorems for the position and velocity of the charged particle in the mechanical particle model introduced by Fontes, Jordão Neves and Sidoravicius (2000).

We consider independent anisotropic bond percolation on \({\mathbb {Z}}^d\times {\mathbb {Z}}^s\) where edges parallel to \({\mathbb {Z}}^d\) are open with probability \(p<p_c({\mathbb {Z}}^d)\) and edges parallel to \({\mathbb {Z}}^s\) are open with probability q, independently of all others. We prove that percolation occurs for \(q\ge 8d^2(p_c({\...

We consider inhomogeneous non-oriented Bernoulli bond percolation on $\Z^d$, where each edge has a parameter, depending on its direction. We prove that, under certain conditions, if the sum of the parameters is strictly greater than 1/2, we have percolation for sufficiently high dimensions. The main tool is a dynamical coupling between the models i...

In this paper we study anisotropic oriented percolation on $\mathbb{Z}^d$ for $d\geq 4$ and show that the local condition for phase transition is closely related to the mean-field condition. More precisely, we show that if the sum of the local probabilities is strictly greater than one and each probability is not too large, then percolation occurs.

We consider inhomogeneous non-oriented Bernoulli bond percolation on Zd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}^d$$\end{document}, where each edge ha...

We consider a particle moving in continuous time as a Markov jump process; its discrete chain is given by an ordinary random walk on ${\mathbb Z}^d$ , and its jump rate at $({\mathbf x},t)$ is given by a fixed function $\varphi$ of the state of a birth-and-death (BD) process at $\\mathbf x$ on time $t$; BD processes at different sites are independe...

We study the phase transition phenomena for long-range oriented percolation and contact process. We study a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution N. We also study an analogous oriented percolation model on the hyper-cubic lattice, here there is a special direction where...

We investigate the problem of percolation of words in a random environment. To each vertex, we independently assign a letter 0 or 1 according to Bernoulli r.v.’s with parameter p. The environment is the resulting graph obtained from an independent long-range bond percolation configuration on Zd−1×Z, d⩾3, where each edge parallel to Zd−1 has length...

We investigate the problem of percolation of words in a random environment. To each vertex, we independently assign a letter $0$ or $1$ according to Bernoulli r.v.'s with parameter $p$. The environment is the resulting graph obtained from an independent long-range bond percolation configuration on $\mathbb{Z}^{d-1} \times \mathbb{Z}$, $d\geq 3$, wh...

We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also study an analogous oriented percolation model on the hyper-cubic lattice, here there is a special direction w...

We consider bond and site Bernoulli Percolation in both the oriented and the non-oriented cases on $\mathbb{Z}^d$ and obtain rigorous upper bounds for the critical points in those models for every dimension $d \geq 3$.

In this paper we study anisotropic oriented percolation on Z^d for d ≥ 4 and show that the local condition for phase transition is closely related to the mean-field condition. More precisely, we show that if the sum of the local probabilities is strictly greater than one and each probability is not too large, then percolation occurs.

We establish central limit theorems for the position and velocity of the charged particle in the mechanical particle model introduced in the paper "Limit velocity for a driven particle in a random medium with mass aggregation" (https://doi.org/10.1016/S0246-0203(00)01059-1).

We consider independent anisotropic bond percolation on $\mathbb{Z}^d\times \mathbb{Z}^s$ where edges parallel to $\mathbb{Z}^d$ are open with probability $p<p_c(\mathbb{Z}^d)$ and edges parallel to $\mathbb{Z}^s$ are open with probability $q$, independently of all others. We prove that percolation occurs for $q\geq 8d^2(p_c(\mathbb{Z}^d)-p)$. This...

We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, and it can be infected or healthy; the infection propagates to healthy neighbors just as in the usual contact process, according to independent exponential times with a fixed rate lambda>0; howeve...