منابع مشابه
Gaussian fluctuations for non-Hermitian random matrix ensembles
Consider an ensemble of N ×N non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded densities and finite (4 + ε) moments, then Z. D. Bai [Ann. Probab. 25 (1997) 494–529] has shown the ensemble to satisfy the circular law: after scaling by a factor of 1...
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In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the framework of random matrix theory. More specifically, by combining the result in [25] with some combinatorial estimates, we are able to prove multi-dimensional centr...
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Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre’s ensemble, in which each matrix element is an independent, identically distributed Gaussian complex random variable. The other is a simpler calculation using N−1...
متن کاملUniversality of random-matrix results for non-Gaussian ensembles.
We study random-matrix ensembles with a non-Gaussian probability distribution P (H) ∼ exp(−Ntr V (H)) where N is the dimension of the matrix H and V (H) is independent of N . Using Efetov’s supersymmetry formalism, we show that in the limit N → ∞ both energy level correlation functions and correlation functions of S-matrix elements are independent of P (H) and hence universal on the scale of th...
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We consider the moment space Mn corresponding to p × p real or complex matrix measures defined on the interval [0, 1]. The asymptotic properties of the first k components of a uniformly distributed vector (S1,n, . . . , Sn,n) ∗ ∼ U(Mn) are studied if n → ∞. In particular, it is shown that an appropriately centered and standardized version of the vector (S1,n, . . . , Sk,n) ∗ converges weakly to...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2006
ISSN: 0091-1798
DOI: 10.1214/009117906000000403