TY - JOUR
T1 - A note on the trace method for random regular graphs
AU - Friedman, Joel
AU - Puder, Doron
N1 - Publisher Copyright:
© 2023, The Hebrew University of Jerusalem.
PY - 2023/9
Y1 - 2023/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85173665828&partnerID=8YFLogxK
U2 - 10.1007/s11856-023-2497-5
DO - 10.1007/s11856-023-2497-5
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AN - SCOPUS:85173665828
SN - 0021-2172
VL - 256
SP - 269
EP - 282
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -