@inproceedings{bc28ff132d664eaf9c68b0ea2398e6ee,
title = "Garland's Technique for Posets and High Dimensional Grassmannian Expanders",
abstract = "Local to global machinery plays an important role in the study of simplicial complexes, since the seminal work of Garland [11] to our days. In this work we develop a local to global machinery for general posets. We show that the high dimensional expansion notions and many recent expansion results have a generalization to posets. Examples are fast convergence of high dimensional random walks generalizing [2,14], an equivalence with a global random walk definition, generalizing [6] and a trickling down theorem, generalizing [20]. In particular, we show that some posets, such as the Grassmannian poset, exhibit qualitatively stronger trickling down effect than simplicial complexes. Using these methods, and the novel idea of posetification to Ramanujan complexes [18,19], we construct a constant degree expanding Grassmannian poset, and analyze its expansion. This it the first construction of such object, whose existence was conjectured in [6].",
keywords = "Garland Method, Grassmannian, High dimensional Expanders, Posets",
author = "Tali Kaufman and Tessler, {Ran J.}",
note = "Publisher Copyright: {\textcopyright} Tali Kaufman and Ran J. Tessler; licensed under Creative Commons License CC-BY 4.0.; 14th Innovations in Theoretical Computer Science Conference, ITCS 2023 ; Conference date: 10-01-2023 Through 13-01-2023",
year = "2023",
month = jan,
day = "1",
doi = "https://doi.org/10.4230/LIPIcs.ITCS.2023.78",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Kalai, {Yael Tauman}",
booktitle = "14th Innovations in Theoretical Computer Science Conference, ITCS 2023",
address = "ألمانيا",
}