Translator Disclaimer
2013 High points for the membrane model in the critical dimension
Alessandra Cipriani
Author Affiliations +
Electron. J. Probab. 18: 1-17 (2013). DOI: 10.1214/EJP.v18-2750

Abstract

In this notice we study the fractal structure of the set of high points for the membrane model in the critical dimension $d=4$. We are able to compute the Hausdorff dimension of the set of points which are atypically high, and also that of clusters, showing that high points tend not to be evenly spread on the lattice. We will see that these results follow closely those obtained by O. Daviaud for the 2-dimensional discrete Gaussian Free Field.

Citation

Download Citation

Alessandra Cipriani. "High points for the membrane model in the critical dimension." Electron. J. Probab. 18 1 - 17, 2013. https://doi.org/10.1214/EJP.v18-2750

Information

Accepted: 23 September 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1286.60092
MathSciNet: MR3109625
Digital Object Identifier: 10.1214/EJP.v18-2750

Subjects:
Primary: 60K35
Secondary: 60G15, 60G60

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.18 • 2013
Back to Top