Reverse Hypercotractivity and Improved Sampling in High Dimensional Expanders

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United States Simons Institute for the Theory of Computing
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Published on ● Video Link: https://www.youtube.com/watch?v=UE1RwhaG0hY


Duration: 57:41
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Yotam Dikstein (Weizmann Institute of Science)
https://simons.berkeley.edu/talks/yotam-dikstein-weizmann-institute-science-2023-06-26
Beyond the Boolean Cube

Hypercontractivity is a fundamental concept in Boolean function analysis. Reverse hypercontractivity is its lesser-known sibling, which is connected with the mixing of small sets. We will introduce reverse hypercontractivity and show that many high-dimensional expanders have this property. Along the way, we will see the connection between mixing and sampling in high-dimensional expanders and discover new Chernoff-like bounds in these marvelous objects.

This talk is based on joint work with Max Hopkins.



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Tags:
Simons Institute
theoretical computer science
UC Berkeley
Computer Science
Theory of Computation
Theory of Computing
Beyond the Boolean Cube
Yotam Dikstein