Lifshitz Tails on the Bethe Lattice: A Combinatorial Approach

@article{Bapst2011LifshitzTO,
  title={Lifshitz Tails on the Bethe Lattice: A Combinatorial Approach},
  author={Victor Bapst and Guilhem Semerjian},
  journal={Journal of Statistical Physics},
  year={2011},
  volume={145},
  pages={51-92}
}
The density of states of disordered hopping models generically exhibits an essential singularity around the edges of its support, known as a Lifshitz tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size limit of random regular graphs, converging locally to the infinite regular tree, for both diagonal and off-diagonal disorder. The exponential growth of the volume and surface of balls on these lattices is an obstacle for the techniques used to characterize the Lifshitz… 
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