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 semiflexible 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.
Publié le : 2009-03-15
Classification:
Random interfaces,
membrane model,
entropic repulsion,
discrete biharmonic Green’s function,
60K35,
82B41,
31B30
@article{1241099926,
author = {Kurt, Noemi},
title = {Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 687-725},
language = {en},
url = {http://dml.mathdoc.fr/item/1241099926}
}
Kurt, Noemi. Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension. Ann. Probab., Tome 37 (2009) no. 1, pp. 687-725. http://gdmltest.u-ga.fr/item/1241099926/