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Key words: Central limit theorem, excited random walk, law of large numbers, positive and negative cookies, recurrence, renewal structure, transience.. AMS 2000 Subject
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 ,
Our aim in in this section is to show that in the case of metabelian groups the lower estimate (11) can be complemented with a similar upper bound. We keep the notation of §2.. §2)
At each time step, the mixer chooses a random vertex adjacent to its current position.. Then, with probability 1/2 it moves to that vertex, and with probability 1/2 it remains at
We give exact criteria for recurrence and transience, thus generalizing results by Benjamini and Wilson for once-excited random walk on Z d and by the author for multi-excited
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
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..
We refine the results of [ 5 ] for dynamical random walk on Z 2 , showing that with probability one the are times when the origin is visited only a.. finite number of times while
