The spectrum of the random environment and localization of noise |
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| Authors: | Dimitris Cheliotis Bálint Virág |
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| Institution: | 1. EURANDOM, Eindhoven University of Technology, L.G. 1.26, P.O. Box 513, 5600?MB, Eindhoven, The Netherlands
2. University of Toronto, 40 St George St., Toronto, ON, M5S 2E4, Canada
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| 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.  | |
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