TY - JOUR
T1 - Limiting empirical spectral distribution for the non-backtracking matrix of an Erd˝os-Rényi random graph
AU - Wang, Ke
AU - Wood, Philip Matchett
N1 - Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.
PY - 2023/11/1
Y1 - 2023/11/1
N2 - In this note, we give a precise description of the limiting empirical spectral distribution for the non-backtracking matrices for an Erdös-Rényi graph assuming tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then, we use Tao and Vu's replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum.
AB - In this note, we give a precise description of the limiting empirical spectral distribution for the non-backtracking matrices for an Erdös-Rényi graph assuming tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then, we use Tao and Vu's replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum.
KW - Random graph
KW - eigenvalues
KW - non-backtracking matrix
UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001093248400001
UR - https://openalex.org/W4385420201
UR - https://www.scopus.com/pages/publications/85166414380
U2 - 10.1017/S096354832300024X
DO - 10.1017/S096354832300024X
M3 - Journal Article
SN - 0963-5483
VL - 32
SP - 956
EP - 973
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 6
ER -