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We prove the CLT for a random walk in a dynamical environment where the states of the environ- ment at different sites are independent Markov chains..
We demonstrate this approach in two ways: we use it to prove that a polynomial approximation exists, reproducing the results of [FU96, U98] in the case the random walk is bounded
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
Keywords: Gaussian random walk; maximum; Riemann zeta function; Euler-Maclaurin summa- tion; equidistant sampling of Brownian motion; finite
For a recurrent random walk in a random environment on a general locally finite connected graph, the mixing measure is unique if there exists a mixing measure Q which is supported
Let us also note that, although we shall only study the particular branching process associated with the cookie random walk, the method presented here could be used to deal with a
Returning to the setting of finite Markov chains, it was mentioned above that the random transposition random walk on the symmetric group S n was the first example for which a
We show that if the random walk kernel associated with the voter model has finite γth moment for some γ > 3, then the evolution of the interface boundaries converge weakly to
