Hypercontractivity on high dimensional expanders

Tom Gur, Noam Lifshitz, Siqi Liu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

We prove hypercontractive inequalities on high dimensional expanders. As in the settings of the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities are effective for global functions, which are functions that are not significantly affected by a restriction of a small set of coordinates. As applications, we obtain Fourier concentration, small-set expansion, and Kruskal-Katona theorems for high dimensional expanders. Our techniques rely on a new approximate Efron-Stein decomposition for high dimensional link expanders.

Original languageAmerican English
Title of host publicationSTOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
EditorsStefano Leonardi, Anupam Gupta
PublisherAssociation for Computing Machinery
Pages176-184
Number of pages9
ISBN (Electronic)9781450392648
DOIs
StatePublished - 6 Sep 2022
Event54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 - Rome, Italy
Duration: 20 Jun 202224 Jun 2022

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022
Country/TerritoryItaly
CityRome
Period20/06/2224/06/22

Bibliographical note

Publisher Copyright:
© 2022 ACM.

Keywords

  • Efron-Stein decomposition
  • Kruskal-Katona theorem
  • epsilon-product space
  • high dimensional expanders
  • hypercontractive inequalities
  • small-set expansion

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