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Furthermore, this representation is irreducible by Proposition 3 , and its representation graph is prime with respect to the Cartesian product since any Cartesian product graph with
Recently much work has been done on the (simple or not) random walk on the unique infinite cluster for the supercritical (bond or site) percolation in Z d (see e.g.. Another
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)
Metric entropy of the class of probability distribution functions on [0, 1] with a k-monotone density is studied through its connection with the small ball probability of
Given a martingale sequence (fn) (possibly vector valued), there is a martingale (gn) on the probability space [0, 1] N , with respect to the filtration L n, the minimal sigma field
Proof : The only problem is to prove formula (4), that is to prove that u is the sum of its Taylor expansion with respect to λ. In the case where A is a complex Banach algebra,
We present a detailed proof of the Dovbysh-Sudakov representation for symmetric positive definite weakly exchangeable infinite random arrays, called Gram-de Finetti matrices, which
This is as a result of the method of proof, using the approach in Barbour (1990), in which the probability metric used for approximation is perhaps not strong enough to metrize