Upper Bounds on the Percolation Correlation Length

Hugo Duminil-Copin, Gady Kozma, Vincent Tassion

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We study the size of the near-critical window for Bernoulli percolation on ℤd. More precisely, we use a quantitative Grimmett–Marstrand theorem to prove that the correlation length, both below and above criticality, is bounded from above by exp (C∕ | p− pc| 2). Improving on this bound would be a further step towards the conjecture that there is no infinite cluster at criticality on ℤd for every d ≥ 2.

Original languageEnglish
Title of host publicationProgress in Probability
EditorsMaria Eulália Vares, Roberto Fernández, Luiz Renato Fontes, Charles M. Newman
PublisherBirkhauser
Chapter16
Pages347-369
Number of pages23
DOIs
StatePublished - 4 Nov 2021

Publication series

NameProgress in Probability
Volume77
ISSN (Print)1050-6977

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics
  • Mathematical Physics
  • Mathematics (miscellaneous)

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