TOPICAL REVIEW: Functionals of Brownian motion, localization and metric graphs

  title={TOPICAL REVIEW: Functionals of Brownian motion, localization and metric graphs},
  author={Alain Comtet and Jean Luc Desbois and Christophe Texier},
  journal={Journal of Physics A},
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded… 
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