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Transience in a Statistical Mechanics model of Random Band Matrices

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We describe a statistical mechanics model on a d-dimensional lattice with a hyperbolic symmetry. This model is expected to reflect spectral properties of random band matrices such as localization and diffusion. The model has a probabilistic formulation as a random walk in a highly correlated random environment. In three dimensions, we prove that this model has a “diffusive phase”. This is joint work with M. Disertori and M. Zirnbauer.

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