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arXiv · 1207.4705

Nonlinear spectral calculus and super-expanders

Manor Mendel·Assaf Naor
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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.

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Manor Mendel, Assaf Naor. 2012-07-19. Nonlinear spectral calculus and super-expanders. https://doi.org/10.1007/s10240-013-0053-2

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