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

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Source: Crossref

Published: Jan 18, 2012

DOI: 10.1017/s0963548311000757

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Source 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.

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