The spectrum of the random environment and localization of noise
Probability
2011-11-10 v1 Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0804.4814,
title = {The spectrum of the random environment and localization of noise},
author = {Dimitrios Cheliotis and Balint Virag},
journal= {arXiv preprint arXiv:0804.4814},
year = {2011}
}
Comments
18 pages, 1 figure