We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeletonâ€¦ (More)

We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3] that a cookie random walk (Xn) has positive or zero speed according to some positive parameter Î± > 1â€¦ (More)

We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on Z. This shows that when the parameter goes to one,â€¦ (More)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching andâ€¦ (More)

On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1 + 1âˆ’p 2 + o(1 âˆ’ p) with respect to the usualâ€¦ (More)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching andâ€¦ (More)

We characterize non-decreasing weight functions for which the associated one-dimensional vertex reinforced random walk (VRRW) localizes on 4 sites. A phase transition appears for weights of order nâ€¦ (More)