Corpus ID: 118145588

The spectrum of random lifts

  title={The spectrum of random lifts},
  author={L. Addario-Berry and S. Griffiths},
  journal={arXiv: Combinatorics},
  • L. Addario-Berry, S. Griffiths
  • Published 2010
  • Mathematics
  • arXiv: Combinatorics
  • For a fixed d-regular graph H, a random n-lift is obtained by replacing each vertex v of H by a "fibre" containing n vertices, then placing a uniformly random matching between fibres corresponding to adjacent vertices of H. We show that with extremely high probability, all eigenvalues of the lift that are not eigenvalues of H, have order O(sqrt(d)). In particular, if H is Ramanujan then its n-lift is with high probability nearly Ramanujan. We also show that any exceptionally large eigenvalues… CONTINUE READING
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