2013/07/02 by Cipriani, Alessandra, Hazra, Rajat Subhra
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1307.0703
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 \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 set of thick points gives full mass to the 4-dimensional Liouville Quantum Gravity measure.