The spectrum of the random environment and localization of noise

D. Cheliotis, B. Virág

Research output: Contribution to journalArticleAcademicpeer-review


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. [three figures omitted] The graphs of the noise covariance structure for d = 4, 3, 2.1 from above.
Original languageEnglish
Pages (from-to)141-158
JournalProbability Theory and Related Fields
Issue number1
Publication statusPublished - 2010


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