The geometry of random walk isomorphism theorems

DOI10.1214/20-AIHP1083zbMath1484.60105arXiv1904.01532OpenAlexW3137143449MaRDI QIDQ2041802

Tyler Helmuth, Andrew Swan, Roland Bauerschmidt

Publication date: 23 July 2021

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.01532

zbMATH Keywords

reinforced random walkssupersymmetryDynkin isomorphismnon-linear sigma modelsvertex-reinforced jump processEisenbaum isomorphismRay-Knight identities

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Local time and additive functionals (60J55)

Related Items (8)

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Cites Work

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• Topics in occupation times and Gaussian free fields
• Cover times, blanket times, and majorizing measures
• Anderson localization for a supersymmetric sigma model
• Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model
• 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
• Gaussian and non-Gaussian random fields associated with Markov processes
• An application of Berezin integration to large deviations
• Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions
• Functional integral representations for self-avoiding walk
• Fourier analysis on a hyperbolic supermanifold with constant curvature
• Self-avoiding walk on a hierarchical lattice in four dimensions
• Vertex-reinforced jump processes on trees and finite graphs
• Branched polymers and dimensional reduction
• Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model
• Universality for 1d random band matrices: sigma-model approximation
• Continuous time vertex-reinforced jump processes
• A Ray-Knight theorem for symmetric Markov processes.
• Thick points of random walk and the Gaussian free field
• Dynkin isomorphism and Mermin-Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process
• Logarithmic correction for the susceptibility of the 4-dimensional weakly self-avoiding walk: a renormalisation group analysis
• Joint density for the local times of continuous-time Markov chains
• Localization for linearly edge reinforced random walks
• Spanning forests andOSP(N|2M) -invariantσ-models
• A new method for the asymptotic evaluation of a class of path integrals
• A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs
• DENSITY OF STATES FOR GUE THROUGH SUPERSYMMETRIC APPROACH
• SUSY Statistical Mechanics and Random Band Matrices
• Introduction to a Renormalisation Group Method
• Markov Processes, Gaussian Processes, and Local Times
• Reinforced random walk

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