25 citations · 36 across the 7 of their papers we have counts for
10 papers
The extinction of the contact process in a one-dimensional random environment with long-range interactions
Pablo A. Gomes, Marcelo R. Hilário, Bernardo N. B. de Lima +1
We study the contact process on the long-range percolation cluster on where each edge is open with probability for . Using a r…
Fluctuation bounds for symmetric random walks on dynamic environments via Russo-Seymour-Welsh
Rangel Baldasso, Marcelo R. Hilario, Daniel Kious +1
In this article, we prove a lower bound for the fluctuations of symmetric random walks on dynamic random environments in dimension in the perturbative regime where the walk…
Phase transition for percolation on a randomly stretched lattice
Marcelo R. Hilario, Marcos Sá, Remy Sanchis +1
Let be a sequence of i.i.d.\ positive random variables. Starting from the usual square lattice replace each horizontal edge that links a site in -th vertica…
Shape theorem and surface fluctuation for Poisson cylinders
Marcelo Hilario, Xinyi Li, Petr Panov
In this work, we prove a shape theorem for Poisson cylinders and give a power law bound on surface fluctuations. We prove that for any , conditioned on the origin b…
Random Walks on Dynamical Random Environments with Non-Uniform Mixing
Oriane Blondel, Marcelo R. Hilario, Augusto Teixeira
In this paper we study random walks on dynamical random environments in dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild m…
Random walk on random walks: low densities
Oriane Blondel, Marcelo R. Hilario, Renato Soares dos Santos +2
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of pertur…
Random walk on random walks: higher dimensions
Oriane Blondel, Marcelo R. Hilario, Renato Soares dos Santos +2
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing resu…
Percolation in Media with Columnar Disorder
Peter Grassberger, Marcelo R. Hilario, Vladas Sidoravicius
We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that t…
Brochette percolation
Hugo Duminil-Copin, Marcelo R. Hilario, Gady Kozma +1
We study bond percolation on the square lattice with one-dimensional inhomogeneities. Inhomogeneities are introduced in the following way: A vertical column on the square lattice i…
Critical fragmentation properties of random drilling: How many random holes need to be drilled to collapse a wooden cube?
K. J. Schrenk, M. R. Hilário, V. Sidoravicius +4
A solid wooden cube fragments into pieces as we sequentially drill holes through it randomly. This seemingly straightforward observation encompasses deep and nontrivial geometrical…