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

DOI10.1007/s00440-018-0855-8zbMath1411.60147arXiv1612.05409OpenAlexW3105796407MaRDI QIDQ1740601

Pierre Tarrès, Silke W. W. Rolles, Franz Merkl

Publication date: 30 April 2019

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.05409

zbMATH Keywords

self-interacting random walkssupersymmetric hyperbolic nonlinear sigma modelvertex-reinforced jump process

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items

Unnamed Item, Representations of the vertex reinforced jump process as a mixture of Markov processes on \(\mathbb{Z}^d\) and infinite trees, Explicit formula for the density of local times of Markov jump processes, The geometry of random walk isomorphism theorems, A note on recurrence of the vertex reinforced jump process and fractional moments localization, Strongly vertex-reinforced jump process on a complete graph

Cites Work

• Unnamed Item
• A comparison of a nonlinear sigma model with general pinning and pinning at one point
• How vertex reinforced jump process arises naturally
• Continuous-time vertex reinforced jump processes on Galton-Watson trees
• Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes
• Anderson localization for a supersymmetric sigma model
• Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model
• Dynamics of vertex-reinforced random walks
• The vertex reinforced jump process and a random Schrödinger operator on finite graphs
• Inverting Ray-Knight identity
• Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model
• Limit theorems for vertex-reinforced jump processes on regular trees
• Fourier analysis on a hyperbolic supermanifold with constant curvature
• Vertex-reinforced jump processes on trees and finite graphs
• Continuous time vertex-reinforced jump processes
• Transience of edge-reinforced random walk
• Localization for linearly edge reinforced random walks
• On the transience of processes defined on Galton-Watson trees
• A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs
• Linearly edge-reinforced random walks