Abstract: The vertex reinforced jump process is a history dependent continuous time process introduced by Werner, which can be mapped into a certain nonlinear sigma model, where spins take values on a supersymmetric hyperbolic manifold. We consider the model on a complete graph with hierarchical interactions and show that in this setting the problem reduces to study a one-dimensional chain with non-constant interactions. This is joint work with S. Rolles and F. Merkl.
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