Reinforced Random Walk and a Supersymmetric Spin System on the Tree

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.

• Speaker: Peter Wildemann (Cambridge)
• Tuesday 28 May 2024, 15:30–16:30
• Venue: MR12.
• Series: Probability; organiser: Jason Miller.