Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model

Merkl, Franz; Rolles, Silke W. W. und Tarres, Pierre (2019): Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model. In: Probability Theory and Related Fields, Bd. 173, Nr. 3-4: S. 1349-1387

Abstract

In this paper, we define an extension of the supersymmetric hyperbolic nonlinear sigma model introduced by Zirnbauer. We show that it arises as a weak joint limit of a time-changed version introduced by Sabot and Tarres of the vertex-reinforced jump process. It describes the asymptotics of rescaled crossing numbers, rescaled fluctuations of local times, asymptotic local times on a logarithmic scale, endpoints of paths, and last exit trees.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0178-8051
• Sprache: Englisch