Hypercontractivity on high dimensional expanders

Tom Gur; Noam Lifshitz; Siqi Liu

doi:10.1145/3519935.3520004

Hypercontractivity on high dimensional expanders

Tom Gur, Noam Lifshitz, Siqi Liu

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 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 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
Pages	176-184
Number of pages	9
ISBN (Electronic)	9781450392648
DOIs	https://doi.org/10.1145/3519935.3520004
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
ISSN (Print)	0737-8017

Conference

Conference	54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022
Country/Territory	Italy
City	Rome
Period	20/06/22 → 24/06/22

Bibliographical note

Funding 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.

Publisher Copyright:
© 2022 ACM.

Keywords

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

Access to Document

10.1145/3519935.3520004

Cite this

Gur, T., Lifshitz, N., & Liu, S. (2022). Hypercontractivity on high dimensional expanders. In S. Leonardi, & A. Gupta (Eds.), STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (pp. 176-184). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3519935.3520004

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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.",

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Gur, T, Lifshitz, N & Liu, S 2022, Hypercontractivity on high dimensional expanders. in S Leonardi & A Gupta (eds), STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 176-184, 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022, Rome, Italy, 20/06/22. https://doi.org/10.1145/3519935.3520004

Hypercontractivity on high dimensional expanders. / Gur, Tom; Lifshitz, Noam; Liu, Siqi.
STOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing. ed. / Stefano Leonardi; Anupam Gupta. Association for Computing Machinery, 2022. p. 176-184 (Proceedings of the Annual ACM Symposium on Theory of Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Hypercontractivity on high dimensional expanders

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