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A local limit theorem for triple connections in subcritical Bernoulli percolation
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  • Published: 08 January 2008

A local limit theorem for triple connections in subcritical Bernoulli percolation

  • M. Campanino1 &
  • M. Gianfelice1 

Probability Theory and Related Fields volume 143, pages 353–378 (2009)Cite this article

Abstract

We prove a local limit theorem for the probability of a site to be connected by disjoint paths to three points in subcritical Bernoulli percolation on \({\mathbb{Z}}^{d},\,d\geq2\) in the limit where their distances tend to infinity.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bologna, P.zza di Porta San Donato 5, 40127, Bologna, Italy

    M. Campanino & M. Gianfelice

Authors
  1. M. Campanino
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  2. M. Gianfelice
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Corresponding author

Correspondence to M. Campanino.

Additional information

M. Campanino and M. Gianfelice are supported by Italian G.N.A.M.P.A. and the University of Bologna Funds for selected research topics.

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Cite this article

Campanino, M., Gianfelice, M. A local limit theorem for triple connections in subcritical Bernoulli percolation. Probab. Theory Relat. Fields 143, 353–378 (2009). https://doi.org/10.1007/s00440-007-0129-3

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  • Received: 10 May 2006

  • Revised: 26 October 2007

  • Published: 08 January 2008

  • Issue Date: March 2009

  • DOI: https://doi.org/10.1007/s00440-007-0129-3

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Keywords

  • Percolation
  • Local limit theorem
  • Decay of connectivities
  • Multidimensional renewal process

Mathematics Subject Classification (2000)

  • 60F15
  • 60K35
  • 82B43
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