Nonlinear spectral calculus and super-expanders

Mendel, Manor; Naor, Assaf

Publications Mathématiques de l'IHÉS, Tome 119 (2014), pp. 1-95.

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.

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