A note on the trace method for random regular graphs

Joel Friedman, Doron Puder*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The main goal of this note is to illustrate the advantage of analyzing the non-backtracking spectrum of a regular graph rather than the ordinary spectrum. We show that by switching to the non-backtracking spectrum, the method of proof used in [Pudl5] yields a bound of 2d−1+2d−1 instead of the original 2d−1+1 on the second largest eigenvalue of a random d-regular graph.

Original languageEnglish
Pages (from-to)269-282
Number of pages14
JournalIsrael Journal of Mathematics
Volume256
Issue number1
DOIs
StatePublished - Sep 2023

Funding

FundersFunder number
Israel Science Poundation1071/16
California Institute for Regenerative Medicine
Horizon 2020 Framework Programme850956
Natural Sciences and Engineering Research Council of Canada
European Research Council

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