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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics