On the Four-Arm Exponent for 2D Percolation at Criticality

Jacob van den Berg; Pierre Nolin

doi:10.1007/978-3-030-60754-8_6

On the Four-Arm Exponent for 2D Percolation at Criticality

Jacob van den Berg^*
, Pierre Nolin

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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Abstract

For two-dimensional percolation at criticality, we discuss the inequality α₄ > 1 for the polychromatic four-arm exponent (and stronger versions, the strongest so far being (formula presented), where α₂ denotes the two-arm exponent). We first briefly discuss five proofs (some of them implicit and not self-contained) from the literature. Then we observe that, by combining two of them, one gets a completely self-contained (and yet quite short) proof.

Original language	English
Title of host publication	In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius
Editors	Maria Eulália Vares, Robert Fernández, Luis Renato Fontes, Charles M. Newman
Publisher	Birkhäuser
Pages	125-145
Number of pages	21
ISBN (Electronic)	9783030607548
ISBN (Print)	9783030607531, 9783030607562
DOIs	https://doi.org/10.1007/978-3-030-60754-8_6
Publication status	Published - 2021

Publication series

Name	Progress in Probability
Volume	77
ISSN (Print)	1050-6977
ISSN (Electronic)	2297-0428

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Funding

Pierre Nolin was partially supported by a GRF grant from the Research Grants Council of the Hong Kong SAR (project CityU11306719).

Funders	Funder number
Research Grants Council, University Grants Committee	CityU11306719

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 10 Reduced Inequalities

Keywords

Arm exponents
Critical percolation

Access to Document

10.1007/978-3-030-60754-8_6

On the Four-Arm Exponent for 2D Percolation at CriticalityFinal published version, 468 KBLicence: Article 25fa Dutch Copyright Act

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Cite this

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abstract = "For two-dimensional percolation at criticality, we discuss the inequality α4 > 1 for the polychromatic four-arm exponent (and stronger versions, the strongest so far being (formula presented), where α2 denotes the two-arm exponent). We first briefly discuss five proofs (some of them implicit and not self-contained) from the literature. Then we observe that, by combining two of them, one gets a completely self-contained (and yet quite short) proof.",

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On the Four-Arm Exponent for 2D Percolation at Criticality. / van den Berg, Jacob; Nolin, Pierre.
In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius. ed. / Maria Eulália Vares; Robert Fernández; Luis Renato Fontes; Charles M. Newman. Birkhäuser, 2021. p. 125-145 (Progress in Probability; Vol. 77).

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

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AU - Nolin, Pierre

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N2 - For two-dimensional percolation at criticality, we discuss the inequality α4 > 1 for the polychromatic four-arm exponent (and stronger versions, the strongest so far being (formula presented), where α2 denotes the two-arm exponent). We first briefly discuss five proofs (some of them implicit and not self-contained) from the literature. Then we observe that, by combining two of them, one gets a completely self-contained (and yet quite short) proof.

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On the Four-Arm Exponent for 2D Percolation at Criticality

Abstract

Publication series

Bibliographical note

Funding

UN SDGs

Keywords

Access to Document

Persistent URL (handle)

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