vol16_pp248-283. 341KB Jun 04 2011 12:05:57 AM
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They introduced the terms “essentially nonnegative matrix” for matrices whose off-diagonal elements are nonnegative and “essentially positive matrix” for essentially
Throughout the variety of forms arising from this family, a particular one seems to be of special interest, since it preserves the symmetric or alternating symmetry structure of
Theorem 4 in [CD95] states that long-range voter models (without swapping) exhibit interface tightness provided that their infection rates q are symmetric, irreducible, and have
(68) The proofs of the following properties are exactly as those of the corresponding results in [32], and are based primarily on the multiplicative mean ergodic theorem Theorem
Moreover, a brief analysis of the proofs reveals that except an asymptotic quadruple inequality for geodesics in ( M, g ) and a central limit property for random walks no
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 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:
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
