MAXIMUM AND ENTROPIC REPULSION FOR A GAUSSIAN MEMBRANE MODEL IN THE CRITICAL DIMENSION

被引：21

作者：

Kurt, Noemi ^{[1
]}

机构：

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

来源：

ANNALS OF PROBABILITY | 2009年 / 37卷 / 02期

基金：

瑞士国家科学基金会;

关键词：

Random interfaces; membrane model; entropic repulsion; discrete biharmonic Green's function; FREE-FIELD; INTERFACE;

D O I：

10.1214/08-AOP417

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Green's function of the discrete Bilaplacian. This is interpreted as a model for a semi-flexible membrane. d = 4 is the critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.

引用

页码：687 / 725

页数：39

共 15 条

[1]

[Anonymous], GRUYTER STUDIES MATH

[2] ENTROPIC REPULSION OF THE LATTICE FREE-FIELD [J].