On the connectivity properties of the complementary set in fractal percolation models

Authors
Menshikov, MV Popov, SY Vachkovskaia, M
Citation
Mv. Menshikov et al., On the connectivity properties of the complementary set in fractal percolation models, PROB TH REL, 119(2), 2001, pp. 176-186
Citations number
15
Categorie Soggetti
Mathematics
Journal title
PROBABILITY THEORY AND RELATED FIELDS
ISSN journal
01788051 → ACNP
Volume
119
Issue
2
Year of publication
2001
Pages
176 - 186
Database
ISI
SICI code
0178-8051(200102)119:2<176:OTCPOT>2.0.ZU;2-U
Abstract
We study the connectivity propel-ties of the complementary set in Poisson m ultiscale percolation model and in Mandelbrot's percolation model in arbitr ary dimension. By using a result about majorizing dependent random fields b y Bernoulli fields, we prove that if the selection parameter is less than c ertain critical value, then, by choosing the scaling parameter large enough , we can assure that there is no percolation in the complementary set.