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

Menshikov, M.V.; Yu, Popov S.; Vachkovskaia, M.

Authors

Popov S. Yu

M. Vachkovskaia



Abstract

We study the connectivity properties of the complementary set in Poisson multiscale percolation model and in Mandelbrot's percolation model in arbitrary dimension. By using a result about majorizing dependent random fields by Bernoulli fields, we prove that if the selection parameter is less than certain critical value, then, by choosing the scaling parameter large enough, we can assure that there is no percolation in the complementary set.

Citation

Menshikov, M., Yu, P. S., & Vachkovskaia, M. (2001). On the connectivity properties of the complementary set in fractal percolation models. Probability Theory and Related Fields, 119(2), 176-186. https://doi.org/10.1007/pl00008757

Journal Article Type Article
Publication Date Feb 1, 2001
Deposit Date May 1, 2007
Journal Probability Theory and Related Fields
Print ISSN 0178-8051
Electronic ISSN 1432-2064
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 119
Issue 2
Pages 176-186
DOI https://doi.org/10.1007/pl00008757

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