The functional integral for quantum systems with Hamiltonians unbounded from below: Michel Carreau and Edward Farhi. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; Sam Gutmann. Department of Mathematics, Northeastern University, Boston, Massachusetts 02115; and Paul F. Mende. Department of Mathematics and Center for Theoretical Physics, Laboratory for Nuclear

Abstract

Random walks and localized excitations on topologically one-dimensional random fractals, such as paths generated by simple random walks in d-dimensional lattices, are studied. These simple systems display a reach scenario of multifractal behavior in both the probability distribution of the random walks and the localization properties of the wave-functions.