Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach

We present a new, large-deviation approach to investigate the critical properties of Anderson model on Bethe lattice close localization transition in thermodynamic limit. Our method allows us study accurately distribution local density states (LDoS) down very small probability tails as ${10}^{\ensuremath{-}50}$, which are completely out reach for standard numerical techniques. perform thorough analysis functional form distributions LDoS, turn be well described by predicted supersymmetric formalism and yields direct transparent estimation correlation volume transition. Such is found diverge exponentially when approached from delocalized regime, singular way that compatible with analytic predictions treatment.