%0 Journal Article
%T The spectrum of the random environment and localization of noise
%A Dimitrios Cheliotis
%A Balint Virag
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s00440-009-0225-7
%X We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized.
%U http://arxiv.org/abs/0804.4814v1