Nonlinear spectral calculus and super-expanders

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

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 Mathématiques de L'Institut des Hautes Scientifiques
Volume119
Issue number1
DOIs
StatePublished - 2014

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Uniformly Convex Space
Expander
Spectral Gap
Normed Space
Calculus
Zigzag
Regular Graph
Decay
Graph in graph theory

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonlinear spectral calculus and super-expanders. / Mendel, Manor; Naor, Assaf.

In: Publications Mathématiques de L'Institut des Hautes Scientifiques, Vol. 119, No. 1, 2014, p. 1-95.

Research output: Contribution to journalArticle

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