Probability density of the 2d percolation cluster perimeter

J. F. Gouyet; S. Havlin

doi:10.1088/0305-4470/21/8/029

Probability density of the 2d percolation cluster perimeter

J. F. Gouyet
, S. Havlin

Department of Physics - at Bar-Ilan University

Laboratoire de Physique de la Matière Condensée

Research output: Contribution to journal › Comment/debate

3 Scopus citations

Abstract

We study the form of the probability density P(r, f) of the end-to-end distance r of a segment of length f of the perimeter of the ZD percolation cluster at criticality. We find that P(r, 1) behaves as P(r, t) ∝ t^−2/d_Hexp, where. The exponent d_H=7/4 is the fractal dimension of the hull (the external perimeter of a percolation cluster). Thisresult fits very well with recent numerical data.

Original language	English
Pages (from-to)	1921-1923
Number of pages	3
Journal	Journal of Physics A: Mathematical and General
Volume	21
Issue number	8
DOIs	https://doi.org/10.1088/0305-4470/21/8/029
State	Published - 21 Apr 1988

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abstract = "We study the form of the probability density P(r, f) of the end-to-end distance r of a segment of length f of the perimeter of the ZD percolation cluster at criticality. We find that P(r, 1) behaves as P(r, t) ∝ t−2/dHexp, where. The exponent dH=7/4 is the fractal dimension of the hull (the external perimeter of a percolation cluster). Thisresult fits very well with recent numerical data.",

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N2 - We study the form of the probability density P(r, f) of the end-to-end distance r of a segment of length f of the perimeter of the ZD percolation cluster at criticality. We find that P(r, 1) behaves as P(r, t) ∝ t−2/dHexp, where. The exponent dH=7/4 is the fractal dimension of the hull (the external perimeter of a percolation cluster). Thisresult fits very well with recent numerical data.

AB - We study the form of the probability density P(r, f) of the end-to-end distance r of a segment of length f of the perimeter of the ZD percolation cluster at criticality. We find that P(r, 1) behaves as P(r, t) ∝ t−2/dHexp, where. The exponent dH=7/4 is the fractal dimension of the hull (the external perimeter of a percolation cluster). Thisresult fits very well with recent numerical data.

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Probability density of the 2d percolation cluster perimeter

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