Displaying similar documents to “The local relaxation flow approach to universality of the local statistics for random matrices”

Universality in the bulk of the spectrum for complex sample covariance matrices

Sandrine Péché (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).

Product of exponentials and spectral radius of random k-circulants

Arup Bose, Rajat Subhra Hazra, Koushik Saha (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider × random -circulant matrices with → ∞ and = () whose input sequence { }≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + ) moment. We study the asymptotic distribution of the spectral radius, when = + 1. For this, we first derive the tail behaviour of the fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we...

Central limit theorems for linear spectral statistics of large dimensional F-matrices

Shurong Zheng (2012)

Annales de l'I.H.P. Probabilités et statistiques

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In many applications, one needs to make statistical inference on the parameters defined by the limiting spectral distribution of an matrix, the product of a sample covariance matrix from the independent variable array ( )×1 and the inverse of another covariance matrix from the independent variable array ( )×2. Here, the two variable arrays are assumed to either both real or both complex. It helps to find the asymptotic distribution of the relevant parameter...

Comparison of order statistics in a random sequence to the same statistics with i.i.d. variables

Jean-Louis Bon, Eugen Păltănea (2005)

ESAIM: Probability and Statistics

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The paper is motivated by the stochastic comparison of the reliability of non-repairable -out-of- systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let be positive independent random variables with common distribution . For λ > 0 and µ > 0, let consider and . Remark that this is no more than a change of scale for each term. For , let us define to be the...