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In this section, we prove results concerning local (i.e., restricted to proper subspaces) vs global linear dependence of operators that will be used in the proof of Theorem 1.5, and
In section 4 we use this coupling to show the uniqueness of the stationary interface, and then finish the proof of theorem 12. Stochastic compactness for the width of
In the case of the Potts model, the present theorem reproduces earlier results of the authors, with a simplified proof, in the case of the symmetric Ising model (where the
We consider a discrete time financial market with proportional transaction costs. These markets have already been widely studied. In particular, a proof of the fundamental theorem
To prove our functional central limit theorem for rescaled martingales, we do not need to work in the canonical setup of the latter result of Jacod and Shiryaev (1987) nor do we have
Our Berry-Esseen results for the number of isolated balls are analogous to the main results of [ 4 ] (in.. the uniform case) and [ 12 ] (in the non-uniform case) for the number
Although the result in [Bourgain et al., 1992] is stated in terms of influences and not in terms of threshold phenom- ena, the proof can be rephrased and slightly adapted to show
Section 3 introduces a box scheme model for problem ( 1 ), and existence and uniqueness of the solution of the approximating problem ( 12 ) is obtained from the fixed point theorem
