Activated Random Walkers: Facts, Conjectures and Challenges (2009)
Dickman, Ronald, Rolla, Leonardo T., Sidoravicius, Vladas
We study a particle system with hopping (random walk) dynamics on the integer lattice $\mathbb Z^d$. The particles can exist in two states, active or inactive (sleeping); only the former can hop. The...
The Discrete and Continuum Broken Line Process (2009)
Rolla, Leonardo T., Sidoravicius, Vladas, Surgailis, Donatas, Vares, Maria E.
In this work we introduce the discrete-space broken line process (with discrete and continues parameter values) and derive some of its properties. We explore polygonal Markov fields techniques...
Absorbing-State Phase Transition for Stochastic Sandpiles and Activated Random Walks (2009)
Rolla, Leonardo T., Sidoravicius, Vladas
We study the long-time behavior of conservative interacting particle systems in $\mathbb Z$: The Activated Random Walk Model for reaction-diffusion systems and the Stochastic Sandpile. Our main...
Fixation for Distributed Clustering Processes (2009)
Hilario, Marcelo R., Louidor, Oren, Newman, Charles M., Rolla, Leonardo T., Sheffield, Scott, Sidoravicius, Vladas
We study a discrete-time resource flow in $Z^d$, where wealthier vertices attract the resources of their less rich neighbors. For any translation-invariant probability distribution of initial...
Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients (2009)
Braga, Gastao A., Furtado, Frederico, Moreira, Jussara M., Rolla, Leonardo T.
In this paper we present an efficient numerical approach based on the Renormalization Group method for the computation of self-similar dynamics. The latter arise, for instance, as the long-time...
Generalized Hammersley Process and Phase Transition for Activated Random Walk Models (2008)
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they...
Generalized Hammersley Process and Phase Transition for Activated Random Walk Models (2008)
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they...
Last Passage Percolation in Macroscopically Inhomogeneous Media (2008)
Rolla, Leonardo T., Teixeira, Augusto Q.
In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a...
The Language LinF for Fractal Specification (2008)
Leonardo T. Rolla, Cristiano G. Rezende, Rodrigo L. Carceroni
This article presents the language LinF for L-System specification. L-Systems are formal string rewriting systems introduced in 1968 by the botanist Aristid Lindenmayer that are used to model fractal...
Last Passage Percolation in Macroscopically Inhomogeneous Media (2008)
Rolla, Leonardo T.; Instituto De Matemática Pura E Aplicada; Leorolla@impa.br, Teixeira, Augusto Q.; Instituto De Matemática Pura E Aplicada; Augusto@impa.br
In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a...
Braga, Gastão A., Furtado, Frederico, Moreira, Jussara M., Rolla, Leonardo T.
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly...
The Language LinF for Fractal Specification (2003)
Leonardo T. Rolla, Cristiano G. Rezende, Rodrigo L. Carceroni
This article presents the language LinF for L-System specifications. L-Systems are formal string rewriting systems introduced in 1968 by the botanist Aristid Lindenmayer that are used to model...