Uniform boundedness of critical crossing probabilities implies hyperscaling

C. Borgs; J. T. Chayes; H. Kesten; J. Spencer

doi:10.1002/(SICI)1098-2418(199910/12)15:3/4<368::AID-RSA9>3.0.CO;2-B

Uniform boundedness of critical crossing probabilities implies hyperscaling

C. Borgs, J. T. Chayes, H. Kesten, J. Spencer

Research output: Contribution to journal › Article › peer-review

Abstract

We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.

Original language	English (US)
Pages (from-to)	368-413
Number of pages	46
Journal	Random Structures and Algorithms
Volume	15
Issue number	3-4
DOIs	https://doi.org/10.1002/(SICI)1098-2418(199910/12)15:3/4<368::AID-RSA9>3.0.CO;2-B
State	Published - 1999

ASJC Scopus subject areas

Software
Mathematics(all)
Computer Graphics and Computer-Aided Design
Applied Mathematics

Access to Document

10.1002/(SICI)1098-2418(199910/12)15:3/4<368::AID-RSA9>3.0.CO;2-B

Cite this

@article{634b0ea6cf10423da369c9c306666e19,

title = "Uniform boundedness of critical crossing probabilities implies hyperscaling",

abstract = "We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.",

author = "C. Borgs and Chayes, {J. T.} and H. Kesten and J. Spencer",

year = "1999",

doi = "10.1002/(SICI)1098-2418(199910/12)15:3/4<368::AID-RSA9>3.0.CO;2-B",

language = "English (US)",

volume = "15",

pages = "368--413",

journal = "Random Structures and Algorithms",

issn = "1042-9832",

publisher = "John Wiley and Sons Ltd",

number = "3-4",

}

TY - JOUR

T1 - Uniform boundedness of critical crossing probabilities implies hyperscaling

AU - Borgs, C.

AU - Chayes, J. T.

AU - Kesten, H.

AU - Spencer, J.

PY - 1999

Y1 - 1999

N2 - We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.

AB - We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.

UR - http://www.scopus.com/inward/record.url?scp=0033459005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033459005&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1098-2418(199910/12)15:3/4<368::AID-RSA9>3.0.CO;2-B

DO - 10.1002/(SICI)1098-2418(199910/12)15:3/4<368::AID-RSA9>3.0.CO;2-B

M3 - Article

AN - SCOPUS:0033459005

SN - 1042-9832

VL - 15

SP - 368

EP - 413

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 3-4

ER -

Uniform boundedness of critical crossing probabilities implies hyperscaling

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this