One-dimensional finite range random walk in random medium and invariant measure equation

A fragmentation occurs in the random permutation when a transposition occurs between two integers in the same σ-cycle, so tree components in the random graph correspond to cycles in

Our aim is to prove the convergence for trajectories of particles chosen according to the Gibbs measure in the near-critical case, in order to explain how happens the transition

Keywords : Random walk in random scenery; Weak limit theorem; Law of the iterated logarithm; Brownian motion in Brownian Scenery; Strong approxima- tion.. AMS Subject Classification

Branching processes with selection of the N rightmost individuals have been the subject of recent studies [7, 10, 12], and several conjectures on this processes remain open, such as

In Section 2 we describe the model of Mandelbrot’s martingale in a random environment, and state for this martingale a variante of Theorems 1.1 and 1.2: see Theorems 2.3 and 2.4,

We obtain estimates for large and moderate deviations for the capacity of the range of a random walk on Z d , in dimension d ≥ 5, both in the upward and downward directions..

In this family of random walks, planar simple random walk, hardly recurrent, is the most recurrent one.. This explains the prevalence of transience results on the

In the eighties, Lawler established estimates on intersection probabilities for random walks, which are relevant tools for estimating the expected capacity of the range (see