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Percolation in a multiscale Boolean model

Abstract : We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the $n^{\textrm{th}}$ copy is $\rho^{-n}$. We prove, under optimal integrability assumptions, that no percolation occurs in the multiscale Boolean model for large enough $\rho$ if the rate of the Boolean model is below some critical value.
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https://hal.archives-ouvertes.fr/hal-00519310
Contributor : Jean-Baptiste Gouéré <>
Submitted on : Wednesday, March 9, 2011 - 9:55:03 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Friday, June 10, 2011 - 3:12:29 AM

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  • HAL Id : hal-00519310, version 3
  • ARXIV : 1009.3719

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Jean-Baptiste Gouéré. Percolation in a multiscale Boolean model. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2014, pp.11(1):281-297. ⟨hal-00519310v3⟩

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