Nonlinear spectral calculus and super-expanders

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

26 Scopus citations

Abstract

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesàro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.

Original languageEnglish (US)
Pages (from-to)1-95
Number of pages95
JournalPublications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume119
Issue number1
DOIs
StatePublished - May 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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