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 language | English |
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Title of host publication | STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing |
Editors | Stefano Leonardi, Anupam Gupta |
Publisher | Association for Computing Machinery |
Pages | 176-184 |
Number of pages | 9 |
ISBN (Electronic) | 9781450392648 |
DOIs | |
State | Published - 6 Sep 2022 |
Event | 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 - Rome, Italy Duration: 20 Jun 2022 → 24 Jun 2022 |
Publication series
Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |
Conference
Conference | 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 |
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Country/Territory | Italy |
City | Rome |
Period | 20/06/22 → 24/06/22 |
Bibliographical note
Publisher Copyright:© 2022 ACM.
Keywords
- Efron-Stein decomposition
- Kruskal-Katona theorem
- epsilon-product space
- high dimensional expanders
- hypercontractive inequalities
- small-set expansion