Displaying similar documents to “The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile”

Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Antonio Auffinger, Gérard Ben Arous, Sandrine Péché (2009)

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

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We study the statistics of the largest eigenvalues of real symmetric and sample covariance matrices when the entries are heavy tailed. Extending the result obtained by Soshnikov in ( (2004) 82–91), we prove that, in the absence of the fourth moment, the asymptotic behavior of the top eigenvalues is determined by the behavior of the largest entries of the matrix.

Large scale behavior of semiflexible heteropolymers

Francesco Caravenna, Giambattista Giacomin, Massimiliano Gubinelli (2010)

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

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We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the ) are modeled in terms of random rotations. We focus on the regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative...

A vectorial expression for Liapounov's central limit theorem.

Ramón Ardanuy, Angel Luis Sánchez (1992)

Extracta Mathematicae

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In this paper we prove two Liapounov's central limit theorems for a sequence of independent p-dimensional random vectors, with mean and variance and covariance matrix ∑n, in cases of both general and uniformly bounded sequence.

Local limit theorems on some non unimodular groups.

Emile Le Page, Marc Peigné (1999)

Revista Matemática Iberoamericana

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Let Gd be the semi-direct product of R*+ and Rd, d ≥ 1 and let us consider the product group Gd,N = Gd x RN, N ≥ 1. For a large class of probability measures μ on Gd,N, one prove that there exists ρ(μ) ∈ ]0,1] such that the sequence of finite measures {(n(N+3)/2 / ρ(μ)n) μ*n...

On the density of some Wiener functionals: an application of Malliavin calculus.

Antoni Sintes Blanc (1992)

Publicacions Matemàtiques

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Using a representation as an infinite linear combination of chi-square independent random variables, it is shown that some Wiener functionals, appearing in empirical characteristic process asymptotic theory, have densities which are tempered in the properly infinite case and exponentially decaying in the finite case.

An asymptotic expansion for the distribution of the supremum of a random walk

M. Sgibnev (2000)

Studia Mathematica

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Let S n be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of S n which takes into account the influence of the roots of the equation 1 - ∫ ℝ e s x F ( d x ) = 0 , F being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace...