TITLE

On asymptotics for the spectrum of the product of two random rectangular matrices

AUTHOR(S)
Tikhomirov, A.
PUB. DATE
July 2011
SOURCE
Siberian Mathematical Journal;Jul2011, Vol. 52 Issue 4, p747
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
On assuming the Lindeberg condition, we prove the convergence of the expected spectral distribution of the product of two independent random rectangular matrices with independent entries to a certain distribution on the unit disk in the complex plane. We obtain an explicit expression for the density of the limit distribution.
ACCESSION #
64588435

 

Related Articles

  • Central limit theorems for a hypergeometric randomly reinforced urn. Crimaldi, Irene // Journal of Applied Probability;Sep2016, Vol. 53 Issue 3, p899 

    We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color, given the past, is...

  • On almost sure convergence of the spectral distribution of a power of a random matrix to the Fuss-Catalan distribution. Alexeev, N. // Journal of Mathematical Sciences;Jul2011, Vol. 176 Issue 2, p112 

    In this paper, we considered a power of a non-Hermitian random matrix and prove that the empirical distribution of its singular values converges to the Fuss-Catalan distribution almost surely. Bibliography: 3 titles.

  • On the universal A.S. central limit theorem. H�rmann, S. // Acta Mathematica Hungarica;Sep2007, Vol. 116 Issue 4, p377 

    Let ( X k ) be a sequence of independent r.v.�s such that for some measurable functions gk : R k ? R a weak limit theorem of the form holds with some distribution function G. By a general result of Berkes and Cs�ki (�universal ASCLT�), under mild technical conditions the...

  • On the Classes of Asymptotic Distributions for the Sums of Record Values (I). Chun Su; Jianxiong Lou; Gang Wei // Journal of Mathematical Sciences;Jun2004, Vol. 121 Issue 5, p2698 

    Explores the classes of the asymptotic distributions of the sums of record values. Properties of the classes; Necessary and sufficient conditions for converging in distribution to different distributions in the classes; Nondegenerate probability distribution.

  • A modified likelihood ratio statistic for some nonregular models. Severini, Thomas A. // Biometrika;Sep2004, Vol. 91 Issue 3, p603 

    Higher‐order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal,...

  • Asymptotic distribution of the sample average value-at-risk in the case of heavy-tailed returns. Stoyanov, Stoyan V.; Rachev, Svetlozar T. // Journal of Applied Functional Analysis;Jan2008, Vol. 3 Issue 1, p443 

    In this paper, we provide a stable limit theorem for the asymptotic distribution of the sample average value-at-risk when the distribution of the underlying random variable X describing portfolio returns is heavy-tailed. We illustrate the convergence rate in the limit theorem assuming that X has...

  • Wigner's Semicircle Law and Free Independence. Rajarama Bhat, B. V. // Resonance: Journal of Science Education;Oct2009, Vol. 14 Issue 10, p970 

    Free probability theory is a mathematical generalization of classical probability theory. For free central limit theorem we get the semicircle law as the limit law. E P Wigner came across this probability distribution while studying random matrices.

  • Asymptotic expansions in the CLT in free probability. Chistyakov, G. P.; Götze, F. // Probability Theory & Related Fields;Oct2013, Vol. 157 Issue 1/2, p107 

    We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of free convolution.

  • A class of rank-based test for left-truncated and right-censored data. Pao-sheng Shen // Annals of the Institute of Statistical Mathematics;Jun2009, Vol. 61 Issue 2, p461 

    A class of rank-based tests is proposed for the two-sample problem with left-truncated and right-censored data. The class contains as special cases the extension of log-rank test and Gehan test. The asymptotic distribution theory of the test is presented. The small-sample performance of the test...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics