The scaling limit of senile reinforced random walk.
The spread of a catalytic branching random walk
We consider a catalytic branching random walk on that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position : For some constant , almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for as goes to infinity.
The Strong Liouville Property for a Class of Random Walks.
The voter model with anti-voter bonds
The -algebra of pasts of a random walk on the orbits of the Bernoulli action of the group .
Théorème central limite local sur les extensions compactes de
Théorèmes de dérivation du type de Lebesgue et continuité presque sûre de certains processus gaussiens
Théorèmes limites pour les marches aléatoires sur le dual de
Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior
Time-space analysis of the cluster-formation in interacting diffusions.
Toward the best constant factor for the Rademacher-Gaussian tail comparison
It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants c1 and c2 such that c2≈1.01 c1. A discussion of relative merits of this result versus limit theorems is given.
Transience of algebraic varieties in linear groups - applications to generic Zariski density
We study the transience of algebraic varieties in linear groups. In particular, we show that a “non elementary” random walk in escapes exponentially fast from every proper algebraic subvariety. We also treat the case where the random walk takes place in the real points of a semisimple split algebraic group and show such a result for a wide family of random walks.As an application, we prove that generic subgroups (in some sense) of linear groups are Zariski dense.
Transience of percolation clusters on wedges.
Transient phenomena for random walks in the absence of the expected value of jumps.
Transient random walk in with stationary orientations
In this paper, we extend a result of Campanino and Pétritis [Markov Process. Relat. Fields 9 (2003) 391–412]. We study a random walk in with random orientations. We suppose that the orientation of the kth floor is given by , where is a stationary sequence of random variables. Once the environment fixed, the random walk can go either up or down or can stay in the present floor (but moving with respect to its orientation). This model was introduced by Campanino and Pétritis in [Markov Process....
Tunnel effect for semiclassical random walk
In this note we describe recent results on semiclassical random walk associated to a probability density which may also concentrate as the semiclassical parameter goes to zero. The main result gives a spectral asymptotics of the close to eigenvalues. This problem was studied in [1] and relies on a general factorization result for pseudo-differential operators. In this note we just sketch the proof of this second theorem. At the end of the note, using the factorization, we give a new proof of the...