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)|
|Number of pages||95|
|Journal||Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques|
|State||Published - May 2014|
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