limiting distribution of eigenvalues

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1: 32.14 Combinatorics

… ►The distribution function

F(s)

given by (32.14.2) arises in random matrix theory where it gives the limiting distribution for the normalized largest eigenvalue in the Gaussian Unitary Ensemble of

n\times n

Hermitian matrices; see Tracy and Widom (1994). …

2: 28.12 Definitions and Basic Properties

… ►

§28.12(i) Eigenvalues $\lambda_{\nu+2n}\left(q\right)$

… ► … ►Two eigenfunctions correspond to each eigenvalue

a=\lambda_{\nu}\left(q\right)

. … ► … ►

3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►of the Dirac delta distribution. … ► … ►These eigenvalues will be assumed distinct, i. … ►By Weyl’s alternative

n_{1}

equals either 1 (the limit point case) or 2 (the limit circle case), and similarly for

n_{2}

. … ►The above results, especially the discussions of deficiency indices and limit point and limit circle boundary conditions, lay the basis for further applications. …

4: 28.2 Definitions and Basic Properties

… ►

§28.2(v) Eigenvalues $a_{n}$ , $b_{n}$

►For given

\nu

and

q

, equation (28.2.16) determines an infinite discrete set of values of

a

, the eigenvalues or characteristic values, of Mathieu’s equation. … ►

Distribution

… ►

Change of Sign of $q$

… ►Table 28.2.2 gives the notation for the eigenfunctions corresponding to the eigenvalues in Table 28.2.1. …