One-dimensional random field Kac's model: localization of the phases.
One-dimensional random field Kac's model: weak large deviations principle.
Oriented site percolation, phase transitions and probability bounds.
Percolation beyond , many questions and a few answers.
Percolation on fuchsian groups
Percolation, Perimetry, Planarity.
Percolation times in two-dimensional models for excitable media.
Percolation transition for some excursion sets.
Phase coexistence in Ising, Potts and percolation models
Phase transition for the frog model.
Prime percolation.
Random spatial growth with paralyzing obstacles
We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with others (there is no ‘inter-green’ competition). The red substance remains passive as long as it is isolated. However, when a green cluster comes in touch with the red substance, it is immediately invaded by the latter, stops growing and starts to act as a red...
Reflected planar brownian motions, intertwining relations and crossing probabilities
Self-dual planar hypergraphs and exact bond percolation thresholds.
SLE et invariance conforme
Les processus de Schramm-Loewner (SLE) induisent des courbes aléatoires du plan complexe, qui vérifient une propriété d’invariance conforme. Ce sont des outils fondamentaux pour la compréhension du comportement asymptotique en régime critique de certains modèles discrets intervenant en physique statistique ; ils ont permis notamment d’établir rigoureusement certaines conjectures importantes dans ce domaine.
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...
Soft local times and decoupling of random interlacements
In this paper we establish a decoupling feature of the random interlacement process at level , . Roughly speaking, we show that observations of restricted to two disjoint subsets and of are approximately independent, once we add a sprinkling to the process by slightly increasing the parameter . Our results differ from previous ones in that we allow the mutual distance between the sets and to be much smaller than their diameters. We then provide an important application of this...
Some properties of annulus SLE.
Strict inequality for phase transition between ferromagnetic and frustrated systems.
The incipient infinite cluster in high-dimensional percolation.