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math.GR2021
Banach Zuk's criterion for partite complexes with application to random groups
Izhar Oppenheim
We prove a Banach version of Żuk's criterion for groups acting on partite simplicial complexes. Using this new criterion we derive a new fixed point theorem for random groups in th…
cs.IT2021
High dimensional expansion implies amplified local testability
Tali Kaufman, Izhar Oppenheim
In this work we show that high dimensional expansion implies locally testable code. Specifically, we define a notion that we call high-dimensional-expanding-system (HDE-system). Th…