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dc.contributor.authorSah, Ashwin
dc.contributor.authorSawhney, Mehtaab
dc.contributor.authorZhao, Yufei
dc.date.accessioned2022-10-18T16:47:13Z
dc.date.available2022-10-18T16:47:13Z
dc.date.issued2020
dc.identifier.urihttps://hdl.handle.net/1721.1/145890
dc.description.abstract<jats:title>Abstract</jats:title> <jats:p>Does every $n$-vertex Cayley graph have an orthonormal eigenbasis all of whose coordinates are $O(1/\sqrt{n})$? While the answer is yes for abelian groups, we show that it is no in general. On the other hand, we show that every $n$-vertex Cayley graph (and more generally, vertex-transitive graph) has an orthonormal basis whose coordinates are all $O(\sqrt{\log n / n})$, and that this bound is nearly best possible. Our investigation is motivated by a question of Assaf Naor, who proved that random abelian Cayley graphs are small-set expanders, extending a classic result of Alon–Roichman. His proof relies on the existence of a bounded eigenbasis for abelian Cayley graphs, which we now know cannot hold for general groups. On the other hand, we navigate around this obstruction and extend Naor’s result to nonabelian groups.</jats:p>en_US
dc.language.isoen
dc.publisherOxford University Press (OUP)en_US
dc.relation.isversionof10.1093/IMRN/RNAA298en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleCayley Graphs Without a Bounded Eigenbasisen_US
dc.typeArticleen_US
dc.identifier.citationSah, Ashwin, Sawhney, Mehtaab and Zhao, Yufei. 2020. "Cayley Graphs Without a Bounded Eigenbasis." International Mathematics Research Notices, 2022 (8).
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.relation.journalInternational Mathematics Research Noticesen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2022-10-18T16:39:01Z
dspace.orderedauthorsSah, A; Sawhney, M; Zhao, Yen_US
dspace.date.submission2022-10-18T16:39:02Z
mit.journal.volume2022en_US
mit.journal.issue8en_US
mit.licenseOPEN_ACCESS_POLICY
mit.metadata.statusAuthority Work and Publication Information Neededen_US


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