Garland's Technique for Posets and High Dimensional Grassmannian Expanders

Tali Kaufman, Ran J. Tessler

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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].

Original languageEnglish
Title of host publication14th Innovations in Theoretical Computer Science Conference, ITCS 2023
EditorsYael Tauman Kalai
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772631
StatePublished - 1 Jan 2023
Event14th Innovations in Theoretical Computer Science Conference, ITCS 2023 - Cambridge, United States
Duration: 10 Jan 202313 Jan 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference14th Innovations in Theoretical Computer Science Conference, ITCS 2023
Country/TerritoryUnited States

Bibliographical note

Funding Information:
Funding Tali Kaufman: Research supported by ERC and BSF. Ran J. Tessler: (incumbent of the Lillian and George Lyttle Career Development Chair) Research was supported by the ISF grant No. 335/19 and by a research grant from the Center for New Scientists of Weizmann Institute.

Publisher Copyright:
© Tali Kaufman and Ran J. Tessler; licensed under Creative Commons License CC-BY 4.0.


  • Garland Method
  • Grassmannian
  • High dimensional Expanders
  • Posets


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