fabio machado - Academia.edu (original) (raw)
Papers by fabio machado
Revista Digital do LAV, 2013
"Este texto aborda uma intervenção artística ocorrida dentro de um projeto que alia as l... more "Este texto aborda uma intervenção artística ocorrida dentro de um projeto que alia as linguagens da escultura e das histórias em quadrinhos. São explicitados alguns referenciais poéticos do trabalho (Gustavo Nakle, Honoré Daumier e Angelo Agostini) e também questões relativas a seus processos de criação e recepção, num diálogo com o humor e os conceitos de ruído comunicacional e de antimonumento. Anti-Monuments between Sculpture and Comics This text emphasizes an artistic intervention occurred inside a project which allies sculpture and comics’ languages. Some of its poetic references (Gustavo Nakle, Honoré Daumier and Angelo Agostini) and questions about its processes of creation and reception are also explicated, on a dialog with humor and with the concepts of communicational noise and anti-monument." DOI: 10.5902/198373487083
Journal of Statistical Physics, 1997
We consider a model of stochastically interacting particles on an infinite strip of ℤ2; in this m... more We consider a model of stochastically interacting particles on an infinite strip of ℤ2; in this model, known as a branching exclusion process, particles jump to each empty neighboring site with rate λ/4 and also can create a new particle with rate 1/4 at each one of these sites. The initial configuration is assumed to have a rightmost particle and we study the process as seen from the rightmost vertical line occupied. We prove that this process has exactly one invariant measure with the property thatH, the number of empty sites to the left of the rightmost particle, has an exponential moment. This refines a result presented by Bramson {eaet al.}, who proved that ford=1,H is finite with probability 1.
In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs) on Z d , kn... more In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs) on Z d , known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, it becomes active too. At time 0 all particles are sleeping, except for that placed at the origin. We prove that the set of the original positions of all the active particles, rescaled by the elapsed time, converges to some compact convex set. In some specific cases we are able to identify (at least partially) this set.
Journal of Applied Probability, 2010
We consider a random walks system on Z in which each active particle performs a nearest-neighbor ... more We consider a random walks system on Z in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove ...
Journal of Applied Probability, 2011
We study four discrete time stochastic systems on N modeling processes of rumour spreading. The i... more We study four discrete time stochastic systems on N modeling processes of rumour spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumour. The appetite in spreading or hearing the rumour is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand -based on those random variables distribution -whether the probability of having an infinite set of individuals knowing the rumour is positive or not.
Brazilian Journal of Probability and Statistics, 2013
We consider a stochastic model for species evolution. A new species is born at rate λ and a speci... more We consider a stochastic model for species evolution. A new species is born at rate λ and a species dies at rate µ.
We study a system of simple random walks on graphs, known as frog model. This model can be descri... more We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1 − p. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for Z d and regular trees.
Bulletin of the Brazilian …, 2006
We study two versions of random walks systems on complete graphs. In the first one, the random wa... more We study two versions of random walks systems on complete graphs. In the first one, the random walks have geometrically distributed lifetimes so we define and identify a non-trivial critical parameter related to the proportion of visited vertices before the process dies out. In the second version, the lifetimes depend on the past of the process in a non-Markovian setup. For that version, we present results obtained from computational analysis, simulations and a mean field approximation. These three approaches match.
Advances in Applied Probability, 2014
We study an interacting random walk system on Z where at time 0 there is an active particle at 0 ... more We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site n ≥ 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left jump probability ln. We give conditions for global survival, local survival and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability pn ∈ [0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases 1/2 − ln ∼ ±1/n α , pn = 1 and 1/2 − ln ∼ ±1/n α , 1 − pn ∼ 1/n β (where α, β > 0).
Revista Digital do LAV, 2013
"Este texto aborda uma intervenção artística ocorrida dentro de um projeto que alia as l... more "Este texto aborda uma intervenção artística ocorrida dentro de um projeto que alia as linguagens da escultura e das histórias em quadrinhos. São explicitados alguns referenciais poéticos do trabalho (Gustavo Nakle, Honoré Daumier e Angelo Agostini) e também questões relativas a seus processos de criação e recepção, num diálogo com o humor e os conceitos de ruído comunicacional e de antimonumento. Anti-Monuments between Sculpture and Comics This text emphasizes an artistic intervention occurred inside a project which allies sculpture and comics’ languages. Some of its poetic references (Gustavo Nakle, Honoré Daumier and Angelo Agostini) and questions about its processes of creation and reception are also explicated, on a dialog with humor and with the concepts of communicational noise and anti-monument." DOI: 10.5902/198373487083
Journal of Statistical Physics, 1997
We consider a model of stochastically interacting particles on an infinite strip of ℤ2; in this m... more We consider a model of stochastically interacting particles on an infinite strip of ℤ2; in this model, known as a branching exclusion process, particles jump to each empty neighboring site with rate λ/4 and also can create a new particle with rate 1/4 at each one of these sites. The initial configuration is assumed to have a rightmost particle and we study the process as seen from the rightmost vertical line occupied. We prove that this process has exactly one invariant measure with the property thatH, the number of empty sites to the left of the rightmost particle, has an exponential moment. This refines a result presented by Bramson {eaet al.}, who proved that ford=1,H is finite with probability 1.
In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs) on Z d , kn... more In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs) on Z d , known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, it becomes active too. At time 0 all particles are sleeping, except for that placed at the origin. We prove that the set of the original positions of all the active particles, rescaled by the elapsed time, converges to some compact convex set. In some specific cases we are able to identify (at least partially) this set.
Journal of Applied Probability, 2010
We consider a random walks system on Z in which each active particle performs a nearest-neighbor ... more We consider a random walks system on Z in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove ...
Journal of Applied Probability, 2011
We study four discrete time stochastic systems on N modeling processes of rumour spreading. The i... more We study four discrete time stochastic systems on N modeling processes of rumour spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumour. The appetite in spreading or hearing the rumour is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand -based on those random variables distribution -whether the probability of having an infinite set of individuals knowing the rumour is positive or not.
Brazilian Journal of Probability and Statistics, 2013
We consider a stochastic model for species evolution. A new species is born at rate λ and a speci... more We consider a stochastic model for species evolution. A new species is born at rate λ and a species dies at rate µ.
We study a system of simple random walks on graphs, known as frog model. This model can be descri... more We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1 − p. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for Z d and regular trees.
Bulletin of the Brazilian …, 2006
We study two versions of random walks systems on complete graphs. In the first one, the random wa... more We study two versions of random walks systems on complete graphs. In the first one, the random walks have geometrically distributed lifetimes so we define and identify a non-trivial critical parameter related to the proportion of visited vertices before the process dies out. In the second version, the lifetimes depend on the past of the process in a non-Markovian setup. For that version, we present results obtained from computational analysis, simulations and a mean field approximation. These three approaches match.
Advances in Applied Probability, 2014
We study an interacting random walk system on Z where at time 0 there is an active particle at 0 ... more We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site n ≥ 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left jump probability ln. We give conditions for global survival, local survival and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability pn ∈ [0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases 1/2 − ln ∼ ±1/n α , pn = 1 and 1/2 − ln ∼ ±1/n α , 1 − pn ∼ 1/n β (where α, β > 0).