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.
We explore some of the connections between the local picture left by the trace of simple random walk on a cylinder (Z/NZ) d × Z, d ≥ 2, running for times of order N 2d and the model of random...
Vacant set of random interlacements and percolation (2009)
We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z d, d ≥ 3. A non-negative parameter u measures how many trajectories enter the picture....
Eth Zürich, Prof Dr, Alain-sol Sznitman
This is just a short note of Thanks to Prof. A.-S. Sznitman who inspired much of the enthusiasm that went into the creation of this thesis, all the people who supported me during this intense time...
Amir Dembo, Alain-sol Sznitman
We study the asymptotic behavior for large N of the disconnection time TN of simple random walk on the discrete cylinder (Z/NZ) d × Z. When d is sufficiently large, we are able to substantially...
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...
Upper bound on the disconnection time of discrete cylinders and random interlacements (2009)
We study the asymptotic behavior for large $N$ of the disconnection time $T_N$ of a simple random walk on the discrete cylinder $(\mathbb{Z}/N\mathbb{Z})^d\times\mathbb{Z}$, when $d\ge2$. We explore...
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...
On the domination of a random walk on a discrete cylinder by random interlacements (2009)
Sznitman, Alain-Sol; ETH Zurich; Sznitman@math.ethz.ch
We consider simple random walk on a discrete cylinder with base a large d-dimensional torus of side-length N, when d is two or more. We develop a stochastic domination control on the local picture...
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...
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...
Random Walks on Discrete Cylinders and Random Interlacements (2008)
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for...
A Lower Bound on the Disconnection Time of a Discrete Cylinder (2008)
Amir Dembo, Alain-sol Sznitman
Abstract. We study the asymptotic behavior for large N of the disconnection time TN of simple random walk on the discrete cylinder (Z/NZ) d × Z. When d is sufficiently large, we are able to...
ON THE DISCONNECTION OF A DISCRETE CYLINDER BY A RANDOM (2008)
Amir Dembo, Alain-sol Sznitman
Abstract We investigate the large N behavior of the time the simple random walk on the discrete cylinder (ZZ=N ZZ)d \Theta ZZ needs to disconnect the discrete cylinder. We show that when d * 2, this...
Giant component and vacant set for random walk on a discrete torus (2008)
Benjamini, Itai, Sznitman, Alain-Sol
We consider random walk on a discrete torus $E$ of side-length $N$, in sufficiently high dimension $d$. We investigate the percolative properties of the vacant set corresponding to the collection of...
ON THE DOMINATION OF RANDOM WALK ON A DISCRETE CYLINDER BY RANDOM INTERLACEMENTS (2008)
We consider simple random walk on a discrete cylinder with base a large d-dimensional torus of side-length N, when d ≥ 2. We develop a stochastic domination control on the local picture left by the...
A lower bound on the disconnection time of a discrete cylinder (2008)
We study the asymptotic behavior for large N of the disconnection time TN of simple random walk on the discrete cylinder (Z/NZ) d × Z, when d ≥ 2. We explore its connection with the model of...
How universal are asymptotics of disconnection times in discrete cylinders? (2007)
We investigate the disconnection time of a simple random walk in a discrete cylinder with a large finite connected base. In a recent article of A. Dembo and the author it was found that for large $N$...
Vacant Set of Random Interlacements and Percolation (2007)
We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z^d, d bigger or equal to 3. A non-negative parameter u measures how many trajectories enter...
A Lower Bound on the Disconnection Time of a Discrete Cylinder (2007)
Dembo, Amir, Sznitman, Alain-Sol
We study the asymptotic behavior for large N of the disconnection time T_N of simple random walk on a discrete cylinder with base a d-dimensional discrete torus of side-length N. When d is...
Giant Component and Vacant Set for Random Walk on a Discrete Torus (2006)
Benjamini, Itai, Sznitman, Alain-Sol
We consider random walk on a discrete torus E of side-length N, in sufficiently high dimension d. We investigate the percolative properties of the vacant set corresponding to the collection of sites...
An Invariance principle for Isotropic Diffusions in Random Environment (2006)
Alain-sol Sznitman, Ofer Zeitouni
We investigate in this work the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of Brownian motion. When the space dimension is three or more, we prove...
On new examples of ballistic random walks in random environment (2003)
In this article we show that random walks in random environment on $\mathbb{Z}^d$, $d \ge3$, with transition probabilities which are $\varepsilon$-perturbations of the simple random walk and such...
On the Satic and Dynamic Points of View for Certain Random Walks in Random Environment (2002)
Bolthausen, Erwin, Sznitman, Alain-Sol
In this work we prove the equivalence between static and dynamic points of views for certain ballistic random walks in random environment on Zd, when d greater than or equal to 4 and the disorder is...
Cut Points And Diffusive Random Walks In Random Environment (2002)
Erwin Bolthausen, Alain-sol Sznitman, Ofer Zeitouni
We study in this work a special class of multi-dimensional random walks in random environment for which we are able to prove in a non-perturbative fashion both a law of large numbers and a functional...
A Law of Large Numbers for Random Walks in Random Environment (1999)
Sznitman, Alain-Sol, Zerner, Martin
We derive a law of large numbers for a class of multidimensional random walks in random environment satisfying a condition which first appeared in the work of Kalikow. The approach is based on the...
Capacity and principal eigenvalues: the method of enlargement of obstacles revisited (1997)
We describe a coarse graining method, which provides lower bounds on the principal Dirichlet eigenvalue of the Laplacian in regions receiving small obstacles, and sharpens the previous method of...
Distance fluctuations and Lyapounov exponents (1996)
We associate certain translation invariant random metrics on $\mathbb{R}^d$ to Brownian motion evolving in a truncated Poissonian potential. These metrics behave over large distances, in an...
Burkholder, Donald L, Pardoux, Etienne, Sznitman, Alain-Sol, Hennequin, Paul-Louis
Incluye bibliografía
On A Class Of Transient Random Walks In Random Environment
: We introduce in this article a class of transient random walks in random environment on Z d . When d 2, these walks are ballistic and we derive a law of large numbers, a central limit theorem and...
Slowdown Estimates And Central Limit Theorem For Random Walks In Random Environment
This work is concerned with asymptotic properties of multi-dimensional random walks in random environment. Under Kalikow's condition, we show a central limit theorem for random walks in random...