The spectrum of the random environment and localization of noise

Details The spectrum of the random environment and localization of noise The spectrum of the random environment and localization of noise

2008-04-30

arxiv.org/abs/0804.4814v1

Probab. Theory Related Fields 148 (2010), no. 1-2, 141-158

Mathematics

Probability

18 pages, 1 figure

Scientific paper

10.1007/s00440-009-0225-7

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.

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