Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion

@article{Khot2018PseudorandomSI,
  title={Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion},
  author={Subhash Khot and Dor Minzer and Shmuel Safra},
  journal={2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2018},
  pages={592-601}
}
We prove that pseudorandom sets in the Grassmann graph have near-perfect expansion. This completes the last missing piece of the proof of the 2-to-2-Games Conjecture (albeit with imperfect completeness). The Grassmann graph has induced subgraphs that are themselves isomorphic to Grassmann graphs of lower orders. A set of vertices is called pseudorandom if its density within all such subgraphs (of constant order) is at most slightly higher than its density in the entire graph. We prove that… 
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