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Marchenko–Pastur measure with aspect ratio gamma
Definition
Assume the Axiom of Countable Choice.
For , set Define the Marchenko–Pastur set function on Borel by where is Lebesgue measure on . The formula defines a finite Borel measure; its total mass is established by the Marchenko–Pastur law below.
Definition references
Bai and Silverstein, Chapter 3, §3.3, printed pp. 52–58 (complete book PDF).
Junyi Liao, Theorem 2.1 and Lemma 2.5, printed pp. 29–34 (complete lecture notes).
Depends on
Used by
- Isotropic minimum-norm risk limits under a positive spectral gap Corollary
- An isotropic finite-fourth-moment design Example
- At aspect one the reciprocal-spectrum limit diverges Example
- Marchenko–Pastur law and edges below aspect one Example
- Structural zeros and the positive edge above aspect one Example
- The Marchenko–Pastur support and closing lower edge at aspect one Example
- The Marchenko–Pastur formula defines a probability law with the fixed-point transform Lemma
- Almost-sure Marchenko–Pastur law for finite-fourth-moment sample covariance matrices Theorem
Dependency tree · two levels
15 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Bai and Silverstein, Spectral Analysis of Large Dimensional Random Matrices, 2nd ed., Chapter 3 (standard reference, not scraped)
- Junyi Liao, Random Matrix Theory, Theorem 2.1 (standard reference, not scraped)