Waiting for a bat to fly by (in polynomial time)

Itai Benjamini, Gady Kozma, László Lovász, Dan Romik, Gábor Tardos

Research output: Contribution to journalArticle

1 Citation (Scopus)


We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the transition matrix. This is not possible in general, but at least the set of eigenvalues can be recovered under fairly general conditions, e.g., when the graph has a node-transitive automorphism group. The main result is that by observing polynomially many returns, it is possible to estimate the spectral gap of such a graph up to a constant factor.

Original languageEnglish
Pages (from-to)673-683
Number of pages11
JournalCombinatorics Probability and Computing
Issue number5
Publication statusPublished - Sep 1 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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