Entropy of entanglement and multifractal exponents for random states
  We relate the entropy of entanglement of ensembles of random vectors to their generalized fractal dimensions. Expanding the von Neumann entropy around its maximum we show that the first order only depends on the participation ratio, while higher orders involve other multifractal exponents. These results can be applied to entanglement behavior near the Anderson transition. 
Olivier Giraud, John Martin and Bertrand Georgeot