Polynomial localization of the 2D-vertex reinforced jump process

DOI10.1214/20-ECP356zbMath1489.60157arXiv1907.07949OpenAlexW3121057339MaRDI QIDQ2064873

Christophe Sabot

Publication date: 6 January 2022

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.07949

zbMATH Keywords

supersymmetric sigma modelsreinforced processesMermin-Wagner estimates

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Quantum field theory on lattices (81T25) Processes in random environments (60K37)

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Cites Work

• Continuous-time vertex reinforced jump processes on Galton-Watson trees
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• De Finetti's theorem for Markov chains
• Fourier analysis on a hyperbolic supermanifold with constant curvature
• Vertex-reinforced jump processes on trees and finite graphs
• Power-law decay of weights and recurrence of the two-dimensional VRJP
• Dynkin isomorphism and Mermin-Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process
• Transience of edge-reinforced random walk
• Localization for linearly edge reinforced random walks
• Translation-invariance of two-dimensional Gibbsian point processes
• Probability on Trees and Networks
• A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs

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