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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
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..
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
Under the same conditions the finite dimensional distributions of the repeat times converge to the arrival times of suitably modified Poisson processes, and random trees derived
Consider a population of branching particles in Z d , such that individuals move independently in discrete time according to a random walk with zero mean and finite second moments,
At the end of this note we show that (2) is not true in three dimensions, i.e., with probability one, the cut points of two independent three dimensional simple random walks
In Section 5.3 we make a cut-off for small times, showing that these times are negligible in the limit as κ → ∞ , perform a space-time scaling and compactification of the
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
