A note on the trace method for random regular graphs

Joel Friedman, Doron Puder

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - Sep 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics


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