Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices
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Junshan Xie
Abstract
We consider the number of eigenvalues which fall into an interval for the complex sample covariance matrices. The central limit theorem and a moderate deviation principle are established when the endpoint of the interval is close to the edge of the spectrum. The proofs depend on the Four Moment Theorem about the local statistics of eigenvalues up to edge, and the rigidity theorem of the eigenvalues for sample covariance matrices.
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Artikel in diesem Heft
- The M-Regular Graph of a Commutative Ring
- Further Properties of the Lattice of Torsion Classes of Abelian Cyclically Ordered Groups
- Free Power-Commutative Groupoids
- On Systems of Independent Sets
- Note on G-Module Structure of Orders
- Semisimple Hopf Algebras of Dimension 2q3
- On the Convergence of a Mapped by a Function
- Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions
- Meromorphic Functions Sharing Pairs of Small Functions
- Sharp Inequalities for Polygamma Functions
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients
- Existence of Ground State Solutions for Hamiltonian Elliptic Systems with Gradient Terms
- Approximate Higher Ring Derivations in Non-Archimedean Banach Algebras
- Characterizations of Banach Spaces which are not Isomorphic to any of their Proper Subspaces
- Operator Inequalities Related to Q-Class Functions
- On a Class of Locally Dually Flat (α,β)–Metrics
- Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices
- A Generalization of Jakubec's Formula
