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In this section we prove Proposition 2.3 on the representation of the canonical Palm distribution of the historical process and we prove Theorem 3 on the properties of the
The main objective in this section is to prove the following theorem concerning the conditional distribution of the number of edges given the colouring..
In this paper, we generalize the asymptotic result of Esseen (1958) concerning the Wasserstein distance of order one in the mean central limit theorem to the Wasserstein distances
Combining Theorem 7, the tensorization property of Beckner type-inequalities, Corollary 8 and Theorem 12 allows to derive dimension-free isoperimetric inequalities for the products
As a consequence of Theorem 3.2, Corollary 3.3 and Lemma 3.4, the following result gives the Hausdorff dimension and packing dimension of the intersection of two independent
We discuss various aspects concerning stochastic domination for the Ising model and the fuzzy Potts model. Next, we consider the fuzzy Potts model and prove that on Z d the fuzzy
We now show how the uniform law of large numbers in Theorem 1.1 can be used to prove the hydrodynamic limits for the system of RWRE as stated in Theorem 1.4.. Proof of Theorem 1.4:
The main step in the proof of Theorem 1 (ii) will be Theorem 10 below, which states that within a cube of appropriate size, the final configuration of the model resembles