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.
|Number of pages
|Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
|Published - May 2014
ASJC Scopus subject areas
- General Mathematics