Thick points for Gaussian free fields with different cut-offs

Authors

Alessandra Cipriani, Weierstrass Institute for Applied Analysis and Stochastics
Rajat Subhra Hazra, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Annales de l'institut Henri Poincare (B) Probability and Statistics

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.

First Page

79

Last Page

97

DOI

10.1214/15-AIHP709

Publication Date

2-1-2017

Comments

Open Access, Green

Recommended Citation

Cipriani, Alessandra and Hazra, Rajat Subhra, "Thick points for Gaussian free fields with different cut-offs" (2017). Journal Articles. 2691.
https://digitalcommons.isical.ac.in/journal-articles/2691