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Decay Properties of the Connectivity for Mixed Long Range Percolation Models on ℤd

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Abstract

In this short note we consider mixed short-long range independent bond percolation models on ℤk+d. Let p uv be the probability that the edge (u,v) will be open. Allowing a x,y-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity τ xy is governed by the probability p xy . The result holds up to the critical point.

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Authors and Affiliations

  1. Departamento de Matemática, UFMG, Caixa Postal 1621, 30161-970, Belo Horizonte, MG, Brazil

    Gastão A. Braga, Leandro M. Ciolleti & Rémy Sanchis

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  1. Gastão A. Braga
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  2. Leandro M. Ciolleti
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  3. Rémy Sanchis
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Correspondence to Gastão A. Braga.

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Braga, G.A., Ciolleti, L.M. & Sanchis, R. Decay Properties of the Connectivity for Mixed Long Range Percolation Models on ℤd . J Stat Phys 129, 587–591 (2007). https://doi.org/10.1007/s10955-007-9347-4

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  • DOI: https://doi.org/10.1007/s10955-007-9347-4

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