Degree lower bounds without hyper-regularity

Develop degree lower bounds for skeletons of high dimensional expanders that remove the hyper-regularity assumption. Specifically, prove super-exponential degree lower bounds for families such as Ramanujan complexes whose links are extremely unbalanced, or otherwise identify refined concentration notions that enable extending the current technique beyond the hyper-regular case.

Background

The paper establishes super-exponential degree lower bounds for certain hyper-regular HDX using sampling results. However, many prominent constructions, including Ramanujan complexes, have highly unbalanced links, and the current method does not apply.

The authors suspect this limitation is technical and suggest that sharper concentration tools might remove the hyper-regularity constraint.