TY - JOUR
T1 - Local Spectral Expansion Approach to High Dimensional Expanders Part II
T2 - Mixing and Geometrical Overlapping
AU - Oppenheim, Izhar
N1 - Funding Information:
The author would like to thank Matthew Kahle and Tali Kaufman for many useful discussions and Alexander Lubotzky for the inspiration to pursue this subject. The author was partially supported by ISF Grant No. 293/18.
Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - We further explore the local-to-global approach for expansion of simplicial complexes that we call local spectral expansion. Specifically, we prove that local expansion in the links implies the global expansion phenomena of mixing and geometric overlapping. Our mixing results also give tighter bounds on the error terms compared to previously known results.
AB - We further explore the local-to-global approach for expansion of simplicial complexes that we call local spectral expansion. Specifically, we prove that local expansion in the links implies the global expansion phenomena of mixing and geometric overlapping. Our mixing results also give tighter bounds on the error terms compared to previously known results.
KW - Geometrical overlapping
KW - High dimensional expanders
KW - Mixing
KW - Simplicial complexes
UR - http://www.scopus.com/inward/record.url?scp=85069914978&partnerID=8YFLogxK
U2 - 10.1007/s00454-019-00117-7
DO - 10.1007/s00454-019-00117-7
M3 - Article
AN - SCOPUS:85069914978
SN - 0179-5376
VL - 64
SP - 1023
EP - 1066
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 3
ER -