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

Merkl, Franz; Rolles, Silke W. W.; 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, Vol. 173, No. 3-4: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0178-8051
• Language: English