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 › peer-review

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)

Access to Document

10.1007/s10240-013-0053-2

Fingerprint Dive into the research topics of 'Nonlinear spectral calculus and super-expanders'. Together they form a unique fingerprint.

Cite this

@article{6ee113e52d9b48158039f504372064a0,

title = "Nonlinear spectral calculus and super-expanders",

abstract = "Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Ces{\`a}ro 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.",

author = "Manor Mendel and Assaf Naor",

year = "2014",

month = may,

doi = "10.1007/s10240-013-0053-2",

language = "English (US)",

volume = "119",

pages = "1--95",

journal = "Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques",

issn = "0073-8301",

publisher = "Springer Verlag",

number = "1",

}

TY - JOUR

T1 - Nonlinear spectral calculus and super-expanders

AU - Mendel, Manor

AU - Naor, Assaf

PY - 2014/5

Y1 - 2014/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84893272196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893272196&partnerID=8YFLogxK

U2 - 10.1007/s10240-013-0053-2

DO - 10.1007/s10240-013-0053-2

M3 - Article

AN - SCOPUS:84893272196

VL - 119

SP - 1

EP - 95

JO - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques

JF - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques

SN - 0073-8301

IS - 1

ER -