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February 2017 Thick points for Gaussian free fields with different cut-offs
Alessandra Cipriani, Rajat Subhra Hazra
Ann. Inst. H. Poincaré Probab. Statist. 53(1): 79-97 (February 2017). DOI: 10.1214/15-AIHP709

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.

Les champs libres gaussiens massifs et sans masse peuvent être décrits comme des processus gaussiens généralisées indexés par un espace fonctionnel approprié. Dans cet article nous abordons différentes approches pour approximer ces champs et nous considérons les propriétés fractales des points épais de leur cut-off. Sous certaines conditions suffisantes, pour un processus gaussien avec variance logarithmique nous étudions l’ensemble des points épais et obtenons leur dimension de Hausdorff. Nous prouvons que différents cut-off des champs libres gaussiens satisfont ces hypothèses. Nous donnons aussi des conditions suffisantes pour comparer les points épais des différents cut-off.

Citation

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Alessandra Cipriani. Rajat Subhra Hazra. "Thick points for Gaussian free fields with different cut-offs." Ann. Inst. H. Poincaré Probab. Statist. 53 (1) 79 - 97, February 2017. https://doi.org/10.1214/15-AIHP709

Information

Received: 5 August 2014; Revised: 14 August 2015; Accepted: 15 August 2015; Published: February 2017
First available in Project Euclid: 8 February 2017

zbMATH: 1361.60036
MathSciNet: MR3606735
Digital Object Identifier: 10.1214/15-AIHP709

Subjects:
Primary: 60G60
Secondary: 60G15

Rights: Copyright © 2017 Institut Henri Poincaré

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Vol.53 • No. 1 • February 2017
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