The probability distribution of the percolation threshold in a large system

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the system goes to infinity, provided that the two widely accepted definitions of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic corrections in the power law for the correlation length. The result is obtained by estimating the rate of decay of tail of the limiting distribution in terms of the correlation length exponent v. All results are rigorously proven in the 2D case. Generalizations for three dimensions are also discussed.

Original languageEnglish (US)
Article number013
Pages (from-to)7127-7133
Number of pages7
JournalJournal of Physics A: Mathematical and General
Volume28
Issue number24
DOIs
StatePublished - 1995

Fingerprint

Percolation Threshold
Correlation Length
Probability distributions
Probability Distribution
thresholds
Limiting Distribution
infinity
Three-dimension
Tail
Logarithmic
Power Law
estimating
Exponent
Infinity
exponents
Decay
Converge
decay

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

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abstract = "We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the system goes to infinity, provided that the two widely accepted definitions of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic corrections in the power law for the correlation length. The result is obtained by estimating the rate of decay of tail of the limiting distribution in terms of the correlation length exponent v. All results are rigorously proven in the 2D case. Generalizations for three dimensions are also discussed.",
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The probability distribution of the percolation threshold in a large system. / Berlyand, Leonid V.; Wehr, J.

In: Journal of Physics A: Mathematical and General, Vol. 28, No. 24, 013, 1995, p. 7127-7133.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The probability distribution of the percolation threshold in a large system

AU - Berlyand, Leonid V.

AU - Wehr, J.

PY - 1995

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N2 - We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the system goes to infinity, provided that the two widely accepted definitions of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic corrections in the power law for the correlation length. The result is obtained by estimating the rate of decay of tail of the limiting distribution in terms of the correlation length exponent v. All results are rigorously proven in the 2D case. Generalizations for three dimensions are also discussed.

AB - We show that the distribution of the percolation threshold in a large finite system does not converge to a Gaussian when the size of the system goes to infinity, provided that the two widely accepted definitions of correlation length are equivalent. The shape of the distribution is thus directly related to the presence or absence of logarithmic corrections in the power law for the correlation length. The result is obtained by estimating the rate of decay of tail of the limiting distribution in terms of the correlation length exponent v. All results are rigorously proven in the 2D case. Generalizations for three dimensions are also discussed.

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