LARGE DEVIATIONS FOR DISCRETE AND CONTINUOUS PERCOLATION

Authors
PENROSE MD PISZTORA A
Citation
Md. Penrose et A. Pisztora, LARGE DEVIATIONS FOR DISCRETE AND CONTINUOUS PERCOLATION, Advances in Applied Probability, 28(1), 1996, pp. 29-52
Citations number
19
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Advances in Applied Probability → ACNP
ISSN journal
00018678
Volume
28
Issue
1
Year of publication
1996
Pages
29 - 52
Database
ISI
SICI code
0001-8678(1996)28:1<29:LDFDAC>2.0.ZU;2-F
Abstract
Motivated by a statistical application, we consider continuum percolat ion in two or more dimensions, restricted to a large finite box, when above the critical point. We derive surface order large deviation esti mates for the volume of the largest cluster and for its intersection w ith the boundary of the box. We also give some natural extensions to k nown, analogous results on lattice percolation.