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arXiv · 1307.0703

Thick points for a Gaussian Free Field in 4 dimensions

Alessandra Cipriani·Rajat Subhra Hazra
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Abstract

This article is concerned with the study of the fractal dimension of thick points for a 4-dimensional Gaussian Free Field. We adopt the definition of Gaussian Free Field on $\R^4$ introduced by Chen and Jakobson (2012) viewed as an abstract Wiener space with underlying Hilbert space $H^2(\R^4)$. We can prove that for $0\leq a \leq 4$ the Hausdorff dimension of the set of $a$-high points is $4-a$. We also show that the set of thick points gives full mass to the 4-dimensional Liouville Quantum Gravity measure.

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Alessandra Cipriani, Rajat Subhra Hazra. 2014-05-07. Thick points for a Gaussian Free Field in 4 dimensions. https://arxiv.org/abs/1307.0703

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