Percolation for the vacant set of random interlacements (2009)
Vladas Sidoravicius, Alain-sol Sznitman
Vladas Sidoravicius would like to thank the FIM for financial support and hospitality during his visitsto ETH. His research was also partially supported by CNPq and FAPERJ.
Percolation for the vacant set of random interlacements (2009)
Vladas Sidoravicius, Alain-sol Sznitman
We investigate random interlacements on Z d, d ≥ 3. This model recently introduced in [8] corresponds to a Poisson cloud on the space of doubly infinite trajectories modulo time-shift tending to...
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...
Connectivity Bounds for the Vacant Set of Random Interlacements (2009)
Sidoravicius, Vladas, Sznitman, Alain-Sol
The model of random interlacements on Z^d, d bigger or equal to 3, was recently introduced in arXiv:0704.2560. A non-negative parameter u parametrizes the density of random interlacements on Z^d. In...
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...
CONNECTIVITY BOUNDS FOR THE VACANT SET OF RANDOM INTERLACEMENTS (2009)
Vladas Sidoravicius, Alain-sol Sznitman
The model of random interlacements on Z d, d ≥ 3, was recently introduced in [4]. A non-negative parameter u parametrizes the density of random interlacements on Z d. In the present note we...
The structure of typical clusters in large sparse random configurations (2008)
Bertoin, Jean, Sidoravicius, Vladas
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The...
Kesten, Harry, Sidoravicius, Vladas
We consider the following problem in one-dimensional diffusion-limited aggregation (DLA). At time $t$, we have an "aggregate" consisting of $\Bbb{Z}\cap[0,R(t)]$ [with $R(t)$ a positive integer]. We...
Percolation for the Vacant Set of Random Interlacements (2008)
Sidoravicius, Vladas, Sznitman, Alain-Sol
We investigate random interlacements on Z^d, d bigger or equal to 3. This model recently introduced in arXiv:0704.2560 corresponds to a Poisson cloud on the space of doubly infinite trajectories...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Vares, Maria Eulalia
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
The structure of typical clusters in large sparse random configurations (2008)
Bertoin, Jean, Sidoravicius, Vladas
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The...
The structure of typical clusters in large sparse random configurations (2008)
Bertoin, Jean, Sidoravicius, Vladas
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
A system of grabbing particles related to Galton-Watson trees (2008)
Bertoin, Jean, Sidoravicius, Vladas, Eulalia Vares, Maria
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: Once a...
A Problem in Last-Passage Percolation (2007)
Kesten, Harry, Sidoravicius, Vladas
Let $\{X(v), v \in \Bbb Z^d \times \Bbb Z_+\}$ be an i.i.d. family of random variables such that $P\{X(v)= e^b\}=1-P\{X(v)= 1\} = p$ for some $b>0$. We consider paths $\pi \subset \Bbb Z^d \times...
On a randomized PNG model with a columnar defect (2007)
Beffara, Vincent, Sidoravicius, Vladas, Vares, Maria Eulalia
We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a...
On a randomized PNG model with a columnar defect (2007)
Beffara, Vincent, Sidoravicius, Vladas, Vares, Maria Eulalia
We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a...
On a randomized PNG model with a columnar defect (2007)
Beffara, Vincent, Sidoravicius, Vladas, Vares, Maria Eulalia
We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a...
On a randomized PNG model with a columnar defect (2007)
Beffara, Vincent, Sidoravicius, Vladas, Vares, Maria Eulalia
We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a...
On a randomized PNG model with a columnar defect (2007)
Beffara, Vincent, Sidoravicius, Vladas, Vares, Maria Eulalia
We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a...
Pinning of polymers and interfaces by random potentials (2006)
Alexander, Kenneth S., Sidoravicius, Vladas
We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. Disorder...
Polymer pinning in a random medium as influence percolation (2006)
Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...
Polymer pinning in a random medium as influence percolation (2006)
Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...
Polymer pinning in a random medium as influence percolation (2006)
Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...
Polymer pinning in a random medium as influence percolation (2006)
Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...
The spread of a rumor or infection in a moving population (2005)
Kesten, Harry, Sidoravicius, Vladas
We consider the following interacting particle system: There is a “gas” of particles, each of which performs a continuous-time simple random walk on ℤd, with jump rate DA. These particles are...
Beffara, Vincent, Sidoravicius, Vladas
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
Beffara, Vincent, Sidoravicius, Vladas
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
Beffara, Vincent, Sidoravicius, Vladas
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
Polymer pinning in a random medium as influence percolation (2005)
Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...
Polymer pinning in a random medium as influence percolation (2005)
Beffara, Vincent, Sidoravicius, Vladas, Spohn, Herbert, Vares, Eulalia
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques,...
Pinning of polymers and interfaces by random potentials (2005)
Alexander, Kenneth S., Sidoravicius, Vladas
We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. Disorder...
Sidoravicius, Vladas, Vares, María Eulália
Incluye bibliografía
Beffara, Vincent, Sidoravicius, Vladas
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
Beffara, Vincent, Sidoravicius, Vladas
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
On Long Range Percolation with Heavy Tails (2004)
Friedli, Sacha; IMPA, Rio De Janeiro; Chach@impa.br, Borge De Lima, Bernardo Nunes; UFMG, Belo Horizonte; Bnblima@mat.ufmg.br, Sidoravicius, Vladas; IMPA, Rio De Janeiro; Vladas@impa.br
Consider independent long range percolation on $mathbf{Z}^d$, $dgeq 2$, where edges of length $n$ are open with probability $p_n$. We show that if $limsup_{ntoinfty}p_n>0,$ then there exists...
On Long Range Percolation with Heavy Tails (2004)
Friedli, Sacha; IMPA, Rio De Janeiro; Chach@impa.br, Borge De Lima, Bernardo Nunes; UFMG, Belo Horizonte; Bnblima@mat.ufmg.br, Sidoravicius, Vladas; IMPA, Rio De Janeiro; Vladas@impa.br
Consider independent long range percolation on $mathbf{Z}^d$, $dgeq 2$, where edges of length $n$ are open with probability $p_n$. We show that if $limsup_{ntoinfty}p_n>0,$ then there exists...
A phase transition in a model for the spread of an infection (2004)
Kesten, Harry, Sidoravicius, Vladas
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B,...
Pimentel, Leandro P. R., Sidoravicius, Vladas.
Instituto de Matemática Pura e Aplicada.
A shape theorem for the spread of an infection (2003)
Kesten, Harry, Sidoravicius, Vladas
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous time simple random walk on the d-dimensional lattice. These particles are...
The spread of a rumor or infection in a moving population (2003)
Kesten, Harry, Sidoravicius, Vladas
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous-time simple random walk on $\mathbb{Z}^d$, with jump rate $D_A$. These...
Nonuniqueness for specifications in $\ell^{2+\epsilon}$ (2003)
Berger, Noam, Hoffman, Christopher, Sidoravicius, Vladas
For every $p>2$, we construct a regular and continuous specification ($g$-function), which has a variation sequence that is in $l^p$ and which admits multiple Gibbs measures. Combined with a recent...
A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models (2003)
Camia, Federico, Newman, Charles M., Sidoravicius, Vladas
We study families of dependent site percolation models on the triangular lattice ${\mathbb T}$ and hexagonal lattice ${\mathbb H}$ that arise by applying certain cellular automata to independent...
Branching Random Walk with Catalysts (2003)
Kesten, Harry; Cornell University; Kesten@math.cornell.edu, Sidoravicius, Vladas; IMPA; Vladas@impa.br
Shnerb et al. (2000), (2001) studied the following system of interacting particles on Zd: There are two kinds of particles, called A-particles and B-particles. The A-particles perform continuous time...
Branching Random Walk with Catalysts (2003)
Kesten, Harry; Cornell University; Kesten@math.cornell.edu, Sidoravicius, Vladas; IMPA; Vladas@impa.br
Shnerb et al. (2000), (2001) studied the following system of interacting particles on Zd: There are two kinds of particles, called A-particles and B-particles. The A-particles perform continuous time...
Percolação de Bernoulli dependente em Z² / (2003)
Lima, Bernardo N. Borges., Sidoravicius, Vladas.
Instituto de Matemática Pura e Aplicada.
Cardy's Formula for some Dependent Percolation Models (2001)
Camia, Federico, Newman, Charles M., Sidoravicius, Vladas
We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular...
Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice (2001)
Camia, Federico, Newman, Charles M., Sidoravicius, Vladas
We investigate zero-temperature dynamics on the hexagonal lattice H for the homogeneous ferromagnetic Ising model with zero external magnetic field and a disordered ferromagnetic Ising model with a...
Percolation of Arbitrary words on the Close-Packed Graph of Z2 (2001)
Kesten, Harry; Cornell University; Kesten@math.cornell.edu, Sidoravicius, Vladas; IMPA; Vladas@impa.br, Zhang, Yu; University Of Colorado; Yzhang@math.uccs.edu
Let $Bbb Z^2_{cp}$ be the close-packed graph of $Bbb Z^2$, that is, the graph obtained by adding to each face of $Bbb Z^2$ its diagonal edges. We consider site percolation on $Bbb Z^2_{cp}$, namely,...
Percolation of Arbitrary words on the Close-Packed Graph of Z2 (2001)
Kesten, Harry; Cornell University; Kesten@math.cornell.edu, Sidoravicius, Vladas; IMPA; Vladas@impa.br, Zhang, Yu; University Of Colorado; Yzhang@math.uccs.edu
Let $Bbb Z^2_{cp}$ be the close-packed graph of $Bbb Z^2$, that is, the graph obtained by adding to each face of $Bbb Z^2$ its diagonal edges. We consider site percolation on $Bbb Z^2_{cp}$, namely,...
Limit velocity for a driven particle in a random medium with mass aggregation (2000)
Fontes, Luiz Renato G., Jordão Neves, Eduardo, Sidoravicius, Vladas
Almost All Words Are Seen In Critical Site Percolation On The Triangular Lattice (1998)
Kesten, Harry; Cornell University; Kesten@math.cornell.edu, Sidoravicius, Vladas; IMPA; Vladas@impa.br, Zhang, Yu; University Of Colorado; Yzhang@math.uccs.edu
We consider critical site percolation on the triangular lattice, that is, we choose $X(v) = 0$ or 1 with probability 1/2 each, independently for all vertices $v$ of the triangular lattice. We say...
Almost All Words Are Seen In Critical Site Percolation On The Triangular Lattice (1998)
Kesten, Harry; Cornell University; Kesten@math.cornell.edu, Sidoravicius, Vladas; IMPA; Vladas@impa.br, Zhang, Yu; University Of Colorado; Yzhang@math.uccs.edu
We consider critical site percolation on the triangular lattice, that is, we choose $X(v) = 0$ or 1 with probability 1/2 each, independently for all vertices $v$ of the triangular lattice. We say...