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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.
Mendel, Manor 1 ; Naor, Assaf 2
@article{PMIHES_2014__119__1_0,
author = {Mendel, Manor and Naor, Assaf},
title = {Nonlinear spectral calculus and super-expanders},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {1--95},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {119},
year = {2014},
doi = {10.1007/s10240-013-0053-2},
zbl = {1306.46021},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-013-0053-2/}
}
TY - JOUR AU - Mendel, Manor AU - Naor, Assaf TI - Nonlinear spectral calculus and super-expanders JO - Publications Mathématiques de l'IHÉS PY - 2014 SP - 1 EP - 95 VL - 119 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-013-0053-2/ DO - 10.1007/s10240-013-0053-2 LA - en ID - PMIHES_2014__119__1_0 ER -
%0 Journal Article %A Mendel, Manor %A Naor, Assaf %T Nonlinear spectral calculus and super-expanders %J Publications Mathématiques de l'IHÉS %D 2014 %P 1-95 %V 119 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-013-0053-2/ %R 10.1007/s10240-013-0053-2 %G en %F PMIHES_2014__119__1_0
Mendel, Manor; Naor, Assaf. Nonlinear spectral calculus and super-expanders. Publications Mathématiques de l'IHÉS, Tome 119 (2014), pp. 1-95. doi: 10.1007/s10240-013-0053-2
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