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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
Indeed, using estimates for the so-called tan points of the simple random walk, introduced in [1] and subse- quently used in [7, 8], it is possible to prove that, when d ≥ 2, the
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices.. This random walk, already known to be transient, has
In the following we give a short description of the standard branching random walk, its intrinsic martingales and an associated multiplicative random walk.. Consider a
For walks on continuous groups, we mention the work of Rosenthal [19] and Porod [17, 18], who obtain total variation rates of convergence for random walks on SO ( n ) and other
We prove the moderate deviation principle for subgraph count statistics of Erd˝ os-Rényi random graphs.. This is equivalent in showing the moderate deviation principle for the trace
We study the entropy of the distribution of the set R n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps.. It is shown that this
Key words: Weak convergence, Bernoulli random walks, Brownian meander, bridge, ex- cursion, peaks.... } be the set of
