A supersymmetric approach to martingales related to the vertex-reinforced jump process

zbMath1364.60068arXiv1511.07157MaRDI QIDQ5346035

Franz Merkl, Silke W. W. Rolles, Margherita Disertori

Publication date: 8 June 2017

Full work available at URL: https://arxiv.org/abs/1511.07157

zbMATH Keywords

martingalenonlinear sigma modelvertex-reinforced jump process

Mathematics Subject Classification ID

Random fields (60G60) Martingales with discrete parameter (60G42) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)

Related Items (9)

Unnamed Item ⋮ A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs ⋮ Dynkin isomorphism and Mermin-Wagner theorems for hyperbolic sigma models and recurrence of the two-dimensional vertex-reinforced jump process ⋮ Random interlacements for vertex-reinforced jump processes ⋮ A note on recurrence of the vertex reinforced jump process and fractional moments localization ⋮ Power-law decay of weights and recurrence of the two-dimensional VRJP ⋮ Multivariate reciprocal inverse Gaussian distributions from the Sabot-Tarrès-Zeng integral ⋮ Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model ⋮ Hitting times of interacting drifted Brownian motions and the vertex reinforced jump process

Cites Work

• A comparison of a nonlinear sigma model with general pinning and pinning at one point
• Anderson localization for a supersymmetric sigma model
• Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model
• Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model
• Fourier analysis on a hyperbolic supermanifold with constant curvature

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