On non-optimally expanding sets in Grassmann graphs
Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra · Israel Journal of Mathematics · 2018
We study the structure of non-expanding sets in the Grassmann graph. We put forth a hypothesis stating that every small set whose expansion is smaller than 1−δ must be correlated with one of a specified list of sets which are isomorphic to smaller Grassmann graphs. We develop a framework of Fourier analysis for analyzing functions over the Grassmann graph, and prove that our hypothesis holds for all sets whose expansion is below 7/8.