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Consider, for instance, the crossing probability of a square in (ordinary) two-dimensional Bernoulli percolation in the scaling limit (i.e., as the lattice spacing goes to zero)
Key words: Central limit theorem, excited random walk, law of large numbers, positive and negative cookies, recurrence, renewal structure, transience.. AMS 2000 Subject
This process will turn out also to be the scaling limit of a point process related to random tilings of the Aztec diamond, studied in (Joh05a) and of a process related to
We will prove that if a limit measure is not absolutely continuous with respect to the Lebesgue measure then the corresponding random walk on the self similar graph does not have
In Section 3, we show that the birth-and-assassination process is the scaling limit, as n goes to infin- ity, of the rumor scotching process when G is the complete graph over n
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
An exact general formula for the expected length of the minimal spanning tree (MST) of a connected (possibly with loops and multiple edges) graph whose edges are assigned
We use this result to show that in dimensions 5 and higher the uniform spanning forest on infinite percolation clusters supported on graphs with infinitely many connected
