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Thick points for a Gaussian Free Field in 4 dimensions

Author

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  • Cipriani, Alessandra
  • Hazra, Rajat Subhra

Abstract

This article is concerned with the study of fractal properties of thick points for a 4-dimensional Gaussian Free Field. We adopt the definition of Gaussian Free Field on R4 introduced by Chen and Jakobson (2012) viewed as an abstract Wiener space with underlying Hilbert space H2(R4). We can prove that for 0≤a≤4, the Hausdorff dimension of the set of a-high points is 4−a. We also show that the thick points give full mass to the Liouville Quantum Gravity measure on R4.

Suggested Citation

  • Cipriani, Alessandra & Hazra, Rajat Subhra, 2015. "Thick points for a Gaussian Free Field in 4 dimensions," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2383-2404.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:6:p:2383-2404
    DOI: 10.1016/j.spa.2015.01.004
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    References listed on IDEAS

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    1. Kurt, Noemi, 2007. "Entropic repulsion for a class of Gaussian interface models in high dimensions," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 23-34, January.
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