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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
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
CENTRAL LIMIT THEOREMS FOR THE PRODUCTS OF RANDOM MATRICES SAMPLED BY A RANDOM WALK.. FR´ ED´ ERIQUE DUHEILLE-BIENVEN
Recently, in [MR07c], we have shown that the edge-reinforced random walk on any locally finite graph has the same distribution as a random walk in a random environment given by
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined
In the opposite case the condition ( 9 ) is never satisfied and all trajectories starting from the curve ( 5 ) go into the region ( 6 ), experience the point of maximal expansion
