Grandes déviations
“Minimal length” multi-channel
Perturbations ponctuelles d'évolutions : construction d'espaces stationnaires
Annealed Lyapounov exponents and large deviations in a poissonian potential. II
Annealed Lyapounov exponents and large deviations in a poissonian potential. I
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 environment on , when . We also derive tail estimates on the probability of slowdowns. These latter estimates are of special interest due to the natural interplay between slowdowns and the presence of traps in the medium. The tail behavior of the renewal time constructed in [25] plays an important role in...
An equation involving local time
Connectivity bounds for the vacant set of random interlacements
The model of random interlacements on ℤ, ≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter parametrizes the density of random interlacements on ℤ. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level , in the non-percolative regime >∗, with ∗ the non-degenerate critical parameter for the percolation of the vacant...
Giant component and vacant set for random walk on a discrete torus
We consider random walk on a discrete torus of side-length , in sufficiently high dimension . We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time . We show that when is chosen small, as tends to infinity, there is with overwhelming probability a unique connected component in the vacant set which contains segments of length const . Moreover, this connected component occupies a non-degenerate...
Cut points and diffusive random walks in random environment
Brownian motion and random obstacles.
On the domination of a random walk on a discrete cylinder by random interlacements.
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