uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Quenched Voronoi percolation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden..
Univ Oxford, Dept Stat, Oxford OX1 3TG, England..
IMPA, Rio De Janeiro, RJ, Brazil..
Univ Geneva, Dept Math, Geneva, Switzerland..
2016 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 286, 889-911 p.Article in journal (Refereed) Published
Resource type
Text
Abstract [en]

We prove that the probability of crossing a large square in quenched Voronoi percolation converges to 1/2 at criticality, confirming a conjecture of Benjamini, Kalai and Schramm from 1999. The main new tools are a quenched version of the box-crossing property for Voronoi percolation at criticality, and an Efron Stein type bound on the variance of the probability of the crossing event in terms of the sum of the squares of the influences. As a corollary of the proof, we moreover obtain that the quenched crossing event at criticality is almost surely noise sensitive.

Place, publisher, year, edition, pages
2016. Vol. 286, 889-911 p.
Keyword [en]
Voronoi percolation, Noise sensitivity, Quenched crossing probabilities
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-268755DOI: 10.1016/j.aim.2015.09.005ISI: 000364615300020OAI: oai:DiVA.org:uu-268755DiVA: diva2:882519
Funder
Swedish Research Council, 637-2013-7302
Available from: 2015-12-15 Created: 2015-12-09 Last updated: 2017-12-01Bibliographically approved

Open Access in DiVA

fulltext(468 kB)58 downloads
File information
File name FULLTEXT01.pdfFile size 468 kBChecksum SHA-512
d92581fe2e6c5b0da18274e74e4dfaeb08bfec88ff0e1310bb729951ee2338d69bb3444fb2c665b4e9e8bcbda6caa4eb2dd956c27420ee4e6f2b45e79201ed8b
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Authority records BETA

Ahlberg, Daniel

Search in DiVA

By author/editor
Ahlberg, Daniel
By organisation
Analysis and Probability Theory
In the same journal
Advances in Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 58 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 287 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf