Cardy's formula for some dependent percolation models

Federico Camia; Charles M. Newman; Vladas Sidoravicius

doi:10.1007/s005740200006

Cardy's formula for some dependent percolation models

Federico Camia, Charles M. Newman, Vladas Sidoravicius

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

Abstract

We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice ℍ (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice double-struck T sign with flips when a site disagrees with six, five and sometimes four of its six neighbors.

Original language	English (US)
Pages (from-to)	147-156
Number of pages	10
Journal	Bulletin of the Brazilian Mathematical Society
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s005740200006
State	Published - Jul 2002

Keywords

Cardy's formula
Cellular automaton
Conformal invariance
Dependent percolation
Hexagonal lattice

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s005740200006

Cite this

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title = "Cardy's formula for some dependent percolation models",

abstract = "We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice ℍ (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice double-struck T sign with flips when a site disagrees with six, five and sometimes four of its six neighbors.",

keywords = "Cardy's formula, Cellular automaton, Conformal invariance, Dependent percolation, Hexagonal lattice",

author = "Federico Camia and Newman, {Charles M.} and Vladas Sidoravicius",

note = "Funding Information: Received 24 December 2001. 1Supported by N.S.F. grant DMS-0102587. 2Supported by N.S.F. grant DMS-0104278. 3Supported by FAPERJ grant E-26/151.905/2000 CNPq and Fundacion Andes.",

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language = "English (US)",

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T1 - Cardy's formula for some dependent percolation models

AU - Camia, Federico

AU - Newman, Charles M.

AU - Sidoravicius, Vladas

N1 - Funding Information: Received 24 December 2001. 1Supported by N.S.F. grant DMS-0102587. 2Supported by N.S.F. grant DMS-0104278. 3Supported by FAPERJ grant E-26/151.905/2000 CNPq and Fundacion Andes.

PY - 2002/7

Y1 - 2002/7

N2 - We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice ℍ (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice double-struck T sign with flips when a site disagrees with six, five and sometimes four of its six neighbors.

AB - We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice ℍ (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice double-struck T sign with flips when a site disagrees with six, five and sometimes four of its six neighbors.

KW - Cardy's formula

KW - Cellular automaton

KW - Conformal invariance

KW - Dependent percolation

KW - Hexagonal lattice

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Cardy's formula for some dependent percolation models

Abstract

Keywords

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