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On the Banach-Space-Valued Azuma Inequality and Small-Set Isoperimetry of Alon–Roichman Graphs

Published online by Cambridge University Press:  18 January 2012

ASSAF NAOR
ASSAF NAOR*
Affiliation:
Courant Institute, 251 Mercer Street, New York, NY 10012, USA (e-mail: naor@cims.nyu.edu)
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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.

Keywords

Primary 05C5005C8060B11
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 4 , July 2012 , pp. 623 - 634
Copyright
Copyright © Cambridge University Press 2012

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