Maximal Bounds on Cartesian Powers of Finite Graphs

Опубликовано 22 июня 2016, 19:16

In the course of their work on the Unique Games Conjecture, Harrow, Kolla, and Schulman proved that the spherical maximal averaging operator on the hypercube satisfies an L 2 bound independent of dimension, published in 2013. Later, Krause extended the bound to all L p with p > 1 and, together with Kolla, we extended the dimension-free bounds to arbitrary finite cliques. We will discuss the classical and immediate contexts for these results and then outline the central ideas of their proofs. Finally, we will present subsequent results and future directions in our research program of identifying analogous asymptotics from a graph's basic structure.