We review results of two previous papers on the asymptotic behavior of finite connection probabilities in three or more dimensions for Bernoulli percolation and the Fortuin–Kasteleyn random-cluster model. In the introduction, we prove a multidimensional renewal theorem that is needed for these results and previous results on Ornstein–Zernike behavior; the proof is significantly simpler than that originally derived by Doney (1966) and those of other subsequent works on this subject.
Campanino, M., Gianfelice, M. (2016). SOME RESULTS ON THE ASYMPTOTIC BEHAVIOR OF FINITE CONNECTION PROBABILITIES IN PERCOLATION. MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS, 4(3), 311-326 [10.2140/memocs.2016.4.311].
SOME RESULTS ON THE ASYMPTOTIC BEHAVIOR OF FINITE CONNECTION PROBABILITIES IN PERCOLATION
CAMPANINO, MASSIMO;
2016
Abstract
We review results of two previous papers on the asymptotic behavior of finite connection probabilities in three or more dimensions for Bernoulli percolation and the Fortuin–Kasteleyn random-cluster model. In the introduction, we prove a multidimensional renewal theorem that is needed for these results and previous results on Ornstein–Zernike behavior; the proof is significantly simpler than that originally derived by Doney (1966) and those of other subsequent works on this subject.| File | Dimensione | Formato | |
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