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.
|Number of pages||19|
|Journal||Annales de l'institut Henri Poincare (B) Probability and Statistics|
|Publication status||Published - 1 Feb 2017|
- Gaussian multiplicative chaos
- Hausdorff dimension
- Liouville quantum gravity
- Thick points