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The above strategy was adopted earlier by one of the authors for branching random walk in random environment [ 10 ]. There, the Markov chain alluded to above is simply the product
This main result of this paper is that Keane’s one-time reinforced random walk on a ladder is recurrent for any positive reinforcement parameter δ
But it is not clear what effect that the perturbations have on the number of visited points, and it is not obvious that the excited random walk will visit n/ log n distinct points
We prove that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean.. We show that
A remarkable and well known result is that the harmonic measure of a transient nearest neighbor random walk on a finitely generated free group is Markovian [6, 19, 25].. This can
activated random walk (ARW) model is an interacting particle system on G , in which the number of particles initially on each vertex is independently distributed according to law µ..
Furthermore, the criterion applies to two important classes of branching random walks and implies that the critical branching random walk is transient resp.. dies
This investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from
