title: Stretched-exponential behavior and random walks on diluted hypercubic lattices.
abstract: Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large-scale simulations the eigenvalue spectra for this stochastic process and calculate explicitly the time evolution for the autocorrelation function and for the return probability, all at criticality, with hypercube dimensions N up to N=28. We show that at long times both relaxation functions can be described by stretched exponentials with exponent 1/3 and a characteristic relaxation time which grows exponentially with dimension N. The numerical eigenvalue spectra are consistent with analytic predictions for a generic sparse network model.
authors.affiliation: Departamento de Física e Biofísica Instituto de Biociências de Botucatu UNESP-Universidade Estadual Paulista Distrito de Rubião Jr. s/n Botucatu, São Paulo 18618-970, Brazil. lemke@ibb.unesp.br
authors.forename: N
authors.initials: N
authors.lastname: Lemke
authors.forename: Ian A
authors.initials: IA
authors.lastname: Campbell