Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions FÎ» and GÎ» of Heckman and Opdam, and sharp estimates of the particular functions F0 and G0.â€¦ (More)

We prove that Vertex Reinforced Random Walk onZwith weight of order k, with Î± âˆˆ [0, 1/2), is either almost surely recurrent or almost surely transient. This improves a previous result of Volkov whoâ€¦ (More)

We study the contact process on the configuration model with a power law degree distribution, when the exponent is smaller than or equal to two. We prove that the extinction time grows exponentiallyâ€¦ (More)

We study a natural continuous time version of excited random walks, introduced by Norris, Rogers and Williams about twenty years ago. We obtain a necessary and sufficient condition for recurrence andâ€¦ (More)

We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of theâ€¦ (More)

Random walks in random sceneries were introduced independently by Kesten and Spitzer [9] and by Borodin [3, 4]. Let S = (Sn)nâ‰¥0 be a random walk in Zd starting at 0, i.e., S0 = 0 and (Sn âˆ’ Snâˆ’1)nâ‰¥1â€¦ (More)

We obtain the convergence in law of a sequence of excited (also called cookies) random walks toward an excited Brownian motion. This last process is a continuous semi-martingale whose drift is aâ€¦ (More)

We study Vertex-Reinforced-Random-Walk (VRRW) on a complete graph with weights of the form w(n) = n, with Î± > 1. Unlike for the EdgeReinforced-Random-Walk, which in this case localizes a.s. on 2â€¦ (More)

We prove that Vertex Reinforced Random Walk on Z with weight of order k Î± , with Î± âˆˆ [0, 1/2), is either almost surely recurrent or almost surely transient. This improves a previous result of Volkovâ€¦ (More)