|
|||||
 |
|
|
|
|
Some results on the
asymptotic behavior of finite connection probabilities in
percolation
Massimo Campanino and Michele Gianfelice
Vol. 4 (2016), No. 3-4, 311–325
|
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. |
Keywords
random-cluster model, Ornstein–Zernike behavior for
connectivities, renormalization, Ruelle operator, local
limit theorem, invariance principle
|
Mathematical Subject Classification 2010
Primary: 60K35, 82B43, 60K15, 60F17
|
Milestones
Received: 1 April 2016
Revised: 1 May 2016
Accepted: 31 May 2016
Published: 17 December 2016
Communicated by Raffaele Esposito
|
Authors |
| Massimo Campanino | |
| Dipartimento di Matematica Università degli Studi di Bologna I-40127 Bologna Italy |
|
| Michele Gianfelice | |
| Dipartimento di Matematica e
Informatica Università della Calabria Campus di Arcavacata I-87036 Arcavacata di Rende Italy |
|
|
