TY - JOUR
T1 - Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model
AU - Merkl, Franz
AU - Rolles, Silke W.W.
AU - Tarrès, Pierre
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/4/5
Y1 - 2019/4/5
N2 - 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 Tarrès 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.
AB - 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 Tarrès 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.
KW - Self-interacting random walks
KW - Supersymmetric hyperbolic nonlinear sigma model
KW - Vertex-reinforced jump process
UR - http://www.scopus.com/inward/record.url?scp=85048963556&partnerID=8YFLogxK
U2 - 10.1007/s00440-018-0855-8
DO - 10.1007/s00440-018-0855-8
M3 - Article
AN - SCOPUS:85048963556
SN - 0178-8051
VL - 173
SP - 1349
EP - 1387
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 3-4
ER -