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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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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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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DOI: https://doi.org/10.1007/s00440-007-0129-3
Keywords
- Percolation
- Local limit theorem
- Decay of connectivities
- Multidimensional renewal process
Mathematics Subject Classification (2000)
- 60F15
- 60K35
- 82B43