Thick points for Gaussian free fields with different cut-offs

Alessandra Cipriani, Rajat Subhra Hazra

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

Massive and massless Gaussian free fields can be described as generalized Gaussian processes indexed by an appropriate space of functions. In this article we study various approaches to approximate these fields and look at the fractal properties of the thick points of their cut-offs. Under some sufficient conditions for a centered Gaussian process with logarithmic variance we study the set of thick points and derive their Hausdorff dimension. We prove that various cut-offs for Gaussian free fields satisfy these assumptions. We also give sufficient conditions for comparing thick points of different cut-offs.

Original languageEnglish
Pages (from-to)79-97
Number of pages19
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume53
Issue number1
DOIs
Publication statusPublished - 1 Feb 2017
Externally publishedYes

Keywords

  • Cut-offs
  • Gaussian multiplicative chaos
  • Hausdorff dimension
  • Liouville quantum gravity
  • Thick points

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