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

Menshikov, M. V. and Popov, S. Yu. and Vachkovskaia, M. (2001) 'On the connectivity properties of the complementary set in fractal percolation models.', Probability theory and related fields., 119 (2). pp. 176-186.

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.

Item Type:Article
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1007/PL00008757
Record Created:01 May 2007
Last Modified:08 Apr 2009 16:30

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