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Eigenvalues of Cayley Graphs [PDF]
Electronic Journal of Combinatorics, 2018 We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
Xiaogang Liu, Sanming Zhou
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Limiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices [PDF]
Annals of Statistics, 2017 We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked eigenvalues, while the other eigenvalues are bounded but ...
T. Cai, Xiao Han, G. Pan
semanticscholar +1 more source
Algebraic conditions and the sparsity of spectrally arbitrary patterns
Special Matrices, 2021 Given a square matrix A, replacing each of its nonzero entries with the symbol * gives its zero-nonzero pattern. Such a pattern is said to be spectrally arbitrary when it carries essentially no information about the eigenvalues of A.
Deaett Louis, Garnett Colin
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Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs [PDF]
Annals of Probability, 2017 We consider inhomogeneous Erd\H{o}s-R\'enyi graphs. We suppose that the maximal mean degree $d$ satisfies $d \ll \log n$. We characterize the asymptotic behavior of the $n^{1 - o(1)}$ largest eigenvalues of the adjacency matrix and its centred version ...
Florent Benaych-Georges +2 more
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Limit theorems for sample eigenvalues in a generalized spiked population model [PDF]
, 2008 In the spiked population model introduced by Johnstone (2001),the population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes).
Bai, Zhidong, Yao, Jian-Feng
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Annales Scientifiques de l’École Normale Supérieure, 2007 48 pages, 2 figures, To appear in Annales de l ...
Favre, Charles, Jonsson, Mattias
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Global bifurcation result and nodal solutions for Kirchhoff-type equation
AIMS Mathematics, 2021 We investigate the global structure of nodal solutions for the Kirchhoff-type problem $ \left\{\begin{array}{ll} -(a+b\int_{0}^{1}|u'|^2dx)u'' = \lambda f(u),\ x\in (0,1),\\[2ex] u(0) = u(1) = 0, \end{array} \right. $ where $ a > 0, b > 0
Fumei Ye, Xiaoling Han
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Bicliques and Eigenvalues [PDF]
Journal of Combinatorial Theory, Series B, 2001 AbstractA biclique in a graph Γ is a complete bipartite subgraph of Γ. We give bounds for the maximum number of edges in a biclique in terms of the eigenvalues of matrix representations of Γ. These bounds show a strong similarity with Lovász's bound ϑ(Γ) for the Shannon capacity of Γ. Motivated by this similarity we investigate bicliques and the bounds
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Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle [PDF]
, 2015 We address the question of determining the eigenvalues $\lambda\_n$ (listed in nondecreasing order, with multiplicities) for which Courant's nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with $n$ nodal domains ...
Bérard, Pierre, Helffer, Bernard
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 We study a sequence of differential operators of high even order whose potentials converge to the Dirac delta-function. One of the types of separated boundary conditions is considered.
Sergei I. Mitrokhin
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