Abstract
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) |
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Pages (from-to) | 1-95 |
Number of pages | 95 |
Journal | Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques |
Volume | 119 |
Issue number | 1 |
DOIs | |
State | Published - May 2014 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Mathematics(all)