Cipriani, Alessandra ; Hazra, Rajat Subhra (2015) Thick points for a Gaussian Free Field in 4 dimensions Stochastic Processes and their Applications, 125 (6). pp. 2383-2404. ISSN 0304-4149
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Official URL: http://doi.org/10.1016/j.spa.2015.01.004
Related URL: http://dx.doi.org/10.1016/j.spa.2015.01.004
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier B.V.. |
| ID Code: | 121063 |
| Deposited On: | 09 Jul 2021 04:53 |
| Last Modified: | 09 Jul 2021 04:53 |
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