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Title: Eigenvalues of the non-backtracking operator detached from the bulk
We describe the non-backtracking spectrum of a stochastic block model with connection probabilities [Formula: see text]. In this regime we answer a question posed in [L. Dall’Amico, R. Couillet and N. Tremblay, Revisiting the Bethe–Hessian: Improved community detection in sparse heterogeneous graphs, in Advances in Neural Information Processing Systems (2019), pp. 4039–4049] regarding the existence of a real eigenvalue “inside” the bulk, close to the location [Formula: see text]. We also introduce a variant of the Bauer–Fike theorem well suited for perturbations of quadratic eigenvalue problems, which could be of independent interest.  more » « less
Award ID(s):
1949617
PAR ID:
10294640
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Random Matrices: Theory and Applications
Volume:
10
Issue:
03
ISSN:
2010-3263
Page Range / eLocation ID:
2150028
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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