English

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.

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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