WIAS Preprint No. 1999, (2014)

Thick points for Gaussian free fields with different cut-offs



Authors

  • Cipriani, Alessandra
  • Hazra, Rajat Subhra

2010 Mathematics Subject Classification

  • 60G60 60G15

Keywords

  • Gaussian multiplicative chaos, cut-offs, Liouville quantum gravity, thick points, Hausdorff dimension

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.

Appeared in

  • Ann. Inst. H. Poincaré Probab. Statist., 53 (2017) pp. 79-97.

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