Random evolutions processes induced by discrete time Markov chains.
Random recursive trees and the Bolthausen-Sznitman coalescent.
Random split of the interval [0,1]
We define two splitting procedures of the interval [0,1], one using uniformly distributed points on the chosen piece and the other splitting a piece in half. We also define two procedures for choosing the piece to be split; one chooses a piece with a probability proportional to its length and the other chooses each piece with equal probability. We analyse the probability distribution of the lengths of the pieces arising from these procedures.
Random sum Limit Theorems for Nonidentically Distributed Random Variables
Random Sums Of Random Vectors
Random Walks in Attractive Potentials: The Case of Critical Drifts
We consider random walks in attractive potentials - sub-additive functions of their local times. An application of a drift to such random walks leads to a phase transition: If the drift is small than the walk is still sub-ballistic, whereas the walk is ballistic if the drift is strong enough. The set of sub-critical drifts is convex with non-empty interior and can be described in terms of Lyapunov exponents (Sznitman, Zerner ). Recently it was shown that super-critical drifts lead to a limiting...
Rate of convergence for a class of RCA estimators
This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.
Rate of Convergence in the Central Limit Theorem and in the Strong Law of Large Numbers for von Mises Statistics.
Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long-range dependence.
Rate of convergence towards a Fréchet type limit distribution
Rate of growth of a transient cookie random walk.
Rates of convergence for minimal distances in the central limit theorem under projective criteria.
Rates of convergence to the local time of a diffusion
Réarrangements convexes des marches aléatoires
Recent advances in invariance principles for stationary sequences.
Rectification à «Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité»
Recurrence and transience of a multi-excited random walk on a regular tree.
Régularité et propriétés limites des fonctions aléatoires
Regularity of the diffusion coefficient matrix for the lattice gas with energy
Regularity of the effective diffusivity of random diffusion with respect to anisotropy coefficient
We show that the effective diffusivity of a random diffusion with a drift is a continuous function of the drift coefficient. In fact, in the case of a homogeneous and isotropic random environment the function is smooth outside the origin. We provide a one-dimensional example which shows that the diffusivity coefficient need not be differentiable at 0.