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||American English|
|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|
|Number of pages||9|
|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
|Name||Proceedings of the Annual ACM Symposium on Theory of Computing|
|Conference||54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022|
|Period||20/06/22 → 24/06/22|
Bibliographical noteFunding Information:
T.G. is supported by the UKRI Future Leaders Fellowship MR/S031545/1. N.L. is supported in part by ERC advanced grant 834735. S.L. is supported in part by the Berkeley Haas Blockchain Initiative and a donation from the Ethereum Foundation.
© 2022 ACM.
- Efron-Stein decomposition
- Kruskal-Katona theorem
- epsilon-product space
- high dimensional expanders
- hypercontractive inequalities
- small-set expansion