On the banach-space-valued azuma inequality and small-set isoperimetry of alon-roichman graphs

  • Authors:

  • Assaf Naor

  • Affiliations:

  • Courant institute, 251 mercer street, new york, ny 10012, usa (e-mail: naor@cims.nyu.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2012

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Abstract

We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrices. In conjunction with a variant of the Azuma inequality for uniformly smooth normed spaces, we deduce improved bounds on the small-set isoperimetry of Abelian Alon-Roichman random Cayley graphs.