2019/07/31 by Simon Coste, Yizhe Zhu
Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Block (permutation group theory) #Complex Network Analysis Techniques #Connection (principal bundle) #Eigenvalues and eigenvectors #Functional Brain Connectivity Studies #Neural dynamics and brain function #Operator (biology) #Quadratic equation #Spectrum (functional analysis) #Stochastic block model #cs.NA #math.CO #math.NA #math.PR
paper · pdf · doi:10.1142/s2010326321500283
published as Random Matrices: Theory and Applications, 10(3), 2150028, 2021 · 15 pages, 4 figures. Minor revision. To appear in Random Matrices: Theory and Applications
openalex created_date 2019/07/23 · arxiv created 2020/07/26 · openalex publication_date 2020/08/07 · arxiv updated 2021/09/13 · openalex updated_date 2026/08/06
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.