Reinforced Random Walk and a Supersymmetric Spin System on the Tree

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• Peter Wildemann (Cambridge)
• Tuesday 28 May 2024, 15:30-16:30
• MR12.

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Motivated by predictions about the Anderson transition, we study two distinct but related models on regular tree graphs: The vertex-reinforced jump process (VRJP), a random walk preferring to jump to previously visited sites, and the H^{2|2}-model, a lattice spin system whose spins take values in a supersymmetric extension of the hyperbolic plane. Both models undergo a phase transition, and our work provides detailed information about the supercritical phase up to the critical point: We show that their order parameter has an essential singularity as one approaches the critical point, in contrast to algebraic divergences typically expected for statistical mechanics models. Moreover, we identify a previously unexpected multifractal intermediate regime in the supercritical phase. This talk is based on arxiv:2309.01221 and is joint work with R??my Poudevigne.

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