|
|||||
|
|
Localization for a Nonlinear Sigma Model in a Strip Related to Vertex Reinforced Jump Processes |
|
| Authors: | Margherita Disertori Franz Merkl Silke W W Rolles |
| Institution: | 1. Laboratoire de Mathématiques Rapha?l Salem, UMR 6085 CNRS, Université de Rouen, Avenue de l’Université, BP.12 Technop?le du Madrillet, 76801, Saint-étienne-du-Rouvray, France 2. Mathematical Institute, University of Munich, Theresienstr. 39, 80333, Munich, Germany 3. Zentrum Mathematik, Bereich M5, Technische Universit?t München, 85747, Garching bei München, Germany |
| Abstract: | We study a lattice sigma model which is expected to reflect Anderson localization and delocalization transition for real symmetric band matrices in 3D, but describes the mixing measure for a vertex reinforced jump process too. For this model we prove exponential localization at any temperature in a strip, and more generally in any quasi-one dimensional graph, with pinning (mass) at only one site. The proof uses a Mermin–Wagner type argument and a transfer operator approach. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |