Thick points for a Gaussian Free Field in 4 dimensions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Cipriani, Alessandra¹  Hazra, Rajat Subhra² 

[1] Weierstrass Inst Berlin, D-10117 Berlin, Germany

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

关键词: KPZ;    Liouville quantum gravity;    Thick points;    Hausdorff dimension;    Abstract Wiener space;    Bilaplacian;   

DOI  :  10.1016/j.spa.2015.01.004

来源: Elsevier

【 摘 要 】

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 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 <= 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 R-4. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free