Translator Disclaimer
March 2020 The maximum of the four-dimensional membrane model
Florian Schweiger
Ann. Probab. 48(2): 714-741 (March 2020). DOI: 10.1214/19-AOP1372

Abstract

We show that the centred maximum of the four-dimensional membrane model on a box of sidelength $N$ converges in distribution. To do so, we use a criterion of Ding, Roy and Zeitouni (Ann. Probab. 45 (2017) 3886–3928) and prove sharp estimates for the Green’s function of the discrete Bilaplacian. These estimates are the main contribution of this work and might also be of independent interest. To derive them, we use estimates for the approximation quality of finite difference schemes as well as results for the Green’s function of the continuous Bilaplacian.

Citation

Download Citation

Florian Schweiger. "The maximum of the four-dimensional membrane model." Ann. Probab. 48 (2) 714 - 741, March 2020. https://doi.org/10.1214/19-AOP1372

Information

Received: 1 April 2019; Published: March 2020
First available in Project Euclid: 22 April 2020

zbMATH: 07199859
MathSciNet: MR4089492
Digital Object Identifier: 10.1214/19-AOP1372

Subjects:
Primary: 60G15
Secondary: 31B30, 60G60, 60G70, 65N06

Rights: Copyright © 2020 Institute of Mathematical Statistics

JOURNAL ARTICLE
28 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 2 • March 2020
Back to Top