Work

The maximum of the four-dimensional membrane model

Year: 2020

Type: article

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.

Source: The Annals of Probability

DOI: 10.1214/19-aop1372

Author: Florian Schweiger

Institution: University of Bonn

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Studienstiftung des Deutschen Volkes, Hausdorff Center for Mathematics

Awards: G1421283785, G3655066931, G4274133347