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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 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
Then, to prove IDLA inner bound, we need to show that for each vertex v ∈ V the Green function from 0 and expected exit time from a ball around 0 of a random walk starting at v ,
In particular, we prove a strong approximation result for such a random walk which, in turn, enables us to establish strong limit theorems, like the joint Strassen type law of
Merkl and Rolles (see [14]) studied the recurrence of the original reinforced random walk, the so-called linearly bond-reinforced random walk, on two-dimensional graphs.. Sellke
Brownian motion, loop-erased random walk, Green’s function esti- mates, excursion Poisson kernel, Fomin’s identity, strong approximation.. Submitted to EJP on March
A central limit theorem for random walk in a random environment on marked Galton-Watson trees.. Gabriel
Keywords: Local time, favourite site, random walk, Wiener process AMS subject classification: 60J55, 60J15, 60J65.. Submitted to EJP on March