Nonlinear spectral calculus and super-expanders
Metric Geometry
2014-09-30 v3 Combinatorics
Functional Analysis
Abstract
Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro 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.
Cite
@article{arxiv.1207.4705,
title = {Nonlinear spectral calculus and super-expanders},
author = {Manor Mendel and Assaf Naor},
journal= {arXiv preprint arXiv:1207.4705},
year = {2014}
}
Comments
Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current paper