Expanders with respect to Hadamard spaces and random graphs

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

It is shown that there exist a sequence of 3-regular graphs {Gn}n=1 and a Hadamard space X such that {Gn}n=1 forms an expander sequence with respect to X, yet random regular graphs are not expanders with respect to X. This answers a question of the second author and Silberman. The graphs {Gn}n=1 are also shown to be expanders with respect to random regular graphs, yielding a deterministic sublineartime constant-factor approximation algorithm for computing the average squared distance in subsets of a random graph. The proof uses the Euclidean cone over a random graph, an auxiliary continuous geometric object that allows for the implementation of martingale methods.

Original languageEnglish (US)
Pages (from-to)1471-1548
Number of pages78
JournalDuke Mathematical Journal
Volume164
Issue number8
DOIs
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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