Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
On the connectivity properties of the complementary set in fractal percolation models
Download PDF
Download PDF
  • Published: February 2001

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

  • M.V. Menshikov1,
  • S.Yu. Popov2 &
  • M. Vachkovskaia2 

Probability Theory and Related Fields volume 119, pages 176–186 (2001)Cite this article

  • 147 Accesses

  • 12 Citations

  • Metrics details

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.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. University of Durham, Department of Mathematical Sciences, South Road, Durham DH1 3LE, UK. e-mail: Mikhail.Menshikov@durham.ac.uk, , , , , , GB

    M.V. Menshikov

  2. Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo, Mail Box 66.281, CEP 05315–970, São Paulo, SP, Brazil. e-mail: popov@ime.usp.br, marina@ime.usp.br, , , , , , BR

    S.Yu. Popov & M. Vachkovskaia

Authors
  1. M.V. Menshikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S.Yu. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Vachkovskaia
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 21 September 1999 / Revised version: 28 February 2000 / Published online: 21 December 2000

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Menshikov, M., Popov, S. & Vachkovskaia, M. On the connectivity properties of the complementary set in fractal percolation models. Probab Theory Relat Fields 119, 176–186 (2001). https://doi.org/10.1007/PL00008757

Download citation

  • Issue Date: February 2001

  • DOI: https://doi.org/10.1007/PL00008757

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Mathematics Subject Classification (2000): 60K35, 60G60, 28A80
  • Key words and phrases: Fractal percolation – Critical probability – Stochastic majorizing
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature