Kurt, N (2009). Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension. The Annals of Probability, 37(2):687-725.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty |
| Language: | English |
| Date: | 2009 |
| Deposited On: | 05 Nov 2009 14:06 |
| Last Modified: | 27 Jun 2022 07:39 |
| Publisher: | Institute of Mathematical Statistics |
| ISSN: | 0091-1798 |
| OA Status: | Hybrid |
| Publisher DOI: | https://doi.org/10.1214/08-AOP417 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2510021 |
Kurt, N