Nonlinear spectral calculus and super-expanders

Manor Mendel; Assaf Naor

doi:10.1007/s10240-013-0053-2

Nonlinear spectral calculus and super-expanders

Manor Mendel, Assaf Naor

Research output: Contribution to journal › Article

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 language	English (US)
Pages (from-to)	1-95
Number of pages	95
Journal	Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume	119
Issue number	1
DOIs	https://doi.org/10.1007/s10240-013-0053-2
State	Published - May 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/s10240-013-0053-2

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Mendel, M., & Naor, A. (2014). Nonlinear spectral calculus and super-expanders. Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, 119(1), 1-95. https://doi.org/10.1007/s10240-013-0053-2

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