Correction to: Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time (Probability Theory and Related Fields, (2011), 149, 3-4, (397-415), 10.1007/s00440-009-0258-y)

Markus Heydenreich; Remco van der Hofstad

doi:10.1007/s00440-019-00929-x

Correction to: Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time (Probability Theory and Related Fields, (2011), 149, 3-4, (397-415), 10.1007/s00440-009-0258-y)

Markus Heydenreich
, Remco van der Hofstad (Corresponding author)

Research output: Contribution to journal › Comment/Letter to the editor › Academic › peer-review

1 Citation (Scopus)

65 Downloads (Pure)

Abstract

In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.

Original language	English
Pages (from-to)	1183-1185
Number of pages	3
Journal	Probability Theory and Related Fields
Volume	175
Issue number	3-4
Early online date	9 Aug 2019
DOIs	https://doi.org/10.1007/s00440-019-00929-x
Publication status	Published - 1 Dec 2019

Funding

The work of RvdH is supported by the Netherlands Organisation for Scientific Research (NWO), through VICI Grant 639.033.806 and the Gravitation NETWORKS Grant 024.002.003. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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title = "Correction to: Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time (Probability Theory and Related Fields, (2011), 149, 3-4, (397-415), 10.1007/s00440-009-0258-y)",

abstract = "In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.",

author = "Markus Heydenreich and \{van der Hofstad\}, Remco",

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language = "English",

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journal = "Probability Theory and Related Fields",

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Correction to: Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time (Probability Theory and Related Fields, (2011), 149, 3-4, (397-415), 10.1007/s00440-009-0258-y). / Heydenreich, Markus; van der Hofstad, Remco (Corresponding author).
In: Probability Theory and Related Fields, Vol. 175, No. 3-4, 01.12.2019, p. 1183-1185.

Research output: Contribution to journal › Comment/Letter to the editor › Academic › peer-review

TY - JOUR

T1 - Correction to

T2 - Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time (Probability Theory and Related Fields, (2011), 149, 3-4, (397-415), 10.1007/s00440-009-0258-y)

AU - Heydenreich, Markus

AU - van der Hofstad, Remco

PY - 2019/12/1

Y1 - 2019/12/1

N2 - In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.

AB - In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.

UR - https://www.scopus.com/pages/publications/85070335906

U2 - 10.1007/s00440-019-00929-x

DO - 10.1007/s00440-019-00929-x

M3 - Comment/Letter to the editor

AN - SCOPUS:85070335906

SN - 0178-8051

VL - 175

SP - 1183

EP - 1185

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 3-4

ER -

Correction to: Random graph asymptotics on high-dimensional tori II: volume, diameter and mixing time (Probability Theory and Related Fields, (2011), 149, 3-4, (397-415), 10.1007/s00440-009-0258-y)

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Random graph asymptotics on high-dimensional tori II. Volume, diameter and mixing time

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