Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model
成果类型：
Article
署名作者：
Merkl, Franz; Rolles, Silke W. W.; Tarres, Pierre
署名单位：
University of Munich; Technical University of Munich; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0855-8
发表日期：
2019
页码：
1349-1387
关键词：
摘要：
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.
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