Nonlinear spectral calculus and super-expanders

Understand

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.