Theory of stochastic canonical equations

By V. Girko. 2001

183 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/43481a2e02d70ad2f68c513bb015f83df35ac251

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Citations in the corpus

A law of large numbers for finite‐range dependent random matrices (2006, methodology): “They also apply to the equations for the limit of the Stieltjes tranform in [HLN05] and the systems of equations in [Gi90, Corollaries 9.3.2 and 10.1.2], under appropriate hypotheses of “finiteness of filter”, as well as many of the pre-limit “Kx cannonical equations” in [ Gi01 ], x2 {1,...,30}, and”
THE EMPIRICAL EIGENVALUE DISTRIBUTION OF A GRAM MATRIX: FROM INDEPENDENCE TO STATIONARITY (2005, methodology): “The proof relies on related results for matrices with independent but not identically distributed entries and substantially differs from related works in the literature (Boutet de Monvel et al. [3], Girko [ 7 ], etc.).”
Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half‐Plane (2015, methodology): “ xj; w 2B(X;C): With this norm B(X;C) is a Banach space. For an operator T on B(X;C) we write kTkfor the induced operator norm. The following result is considered folklore in the literature (see e.g. [8, 23, 26, 27, 28]). For completeness we include its proof, adjusted to our setup, in the Appendix ”
A CLT FOR INFORMATION-THEORETIC STATISTICS OF GRAM RANDOM MATRICES WITH A GIVEN VARIANCE PROFILE (2007, unknown): “It is a direct consequence of [17, Sections 2 and 4] (see also [11]): Theorem 2.”
Spectral convergence for a general class of random matrices (2011, result): “The reader is also referred to [5] for similar results and other random matrix models.”
A Simple Approach to the Global Regime of Gaussian Ensembles of Random Matrices (2005, background): “scheme, outlined below and dated to [11] (see also [ 6 , 13]).”
Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels Under Limited Feedback (2009, background): “…deﬁned as in (2), where we assume that T N , R N and Q N have uniformly bounded spectral norm (with respect to N ), as ( n, N ) grow large with ratio β ( N ) almost surely, with m ◦ B N , Q N ( z ) given by and e ( z ) is the unique solution of with positive imaginary part if ℑ [ z ] > 0 , with…”
On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution (2009, methodology): “random variables of zero mean and unit variance (see [4, 16, 20, 24, 26] and references therein).”
Free Probability and Random Matrices (2014, background): “For a more extensive list of contributions in this context we refer to the books [3, 17, 20, 40].”
The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile (2004, background): “Σn = Yn +Λn, is a particular case of the general case studied in ([8], Chapter 7, equation K7) for which there exists a limiting distribution for the empirical distribution of the eigenvalues.”
Around the circular law (2011, background): “2 remains valid for random matrices with independent rows provided some natural hypotheses [57].”