Critical exponents of planar gradient percolation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)1748-1776
Journal / PublicationAnnals of Probability
Volume36
Issue number5
Online published11 Sept 2008
Publication statusPublished - 2008
Externally publishedYes

Link(s)

DOI

DOI
Check@CityULib
Link to Scopus https://www.scopus.com/record/display.uri?eid=2-s2.0-53049091843&origin=recordpage
Permanent Link https://scholars.cityu.edu.hk/en/publications/publication(73269412-7ec5-4a70-bf0b-6cafe689d9d0).html

Abstract

We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this model. More precisely, we describe the fluctuations of the interfaces around their (straight) scaling limits, and the expected and typical lengths of these interfaces. These results build on the recent results for critical percolation on this lattice by Smirnov, Lawler, Schramm and Werner, and on the scaling ideas developed by Kesten.

Research Area(s)

  • Critical exponents, Gradient percolation, Inhomogeneous percolation, Random interface

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Publication fingerprints text

100
Gradient Mathematics
82
Scaling limit Mathematics
82
Triangular lattice Mathematics
68
Critical exponents Mathematics
67
Straight Mathematics
55
Linearly Mathematics
52
Scaling Mathematics
50
Fluctuations Mathematics
34
Model Mathematics
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Citation Format(s)

[ RIS ] [ BibTeX ]
Critical exponents of planar gradient percolation. / Nolin, Pierre.
In: Annals of Probability, Vol. 36, No. 5, 2008, p. 1748-1776.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review