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Limiting empirical distribution for eigenvalues of products of random rectangular matrices

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  • Zeng, Xingyuan

Abstract

We study the empirical spectral distribution of a product AN(m)=A1⋯Am of m random rectangular matrices with i.i.d. complex Gaussian entries. The product ensemble is of dimension N×N, and the rectangular matrix Aj is of size Nj×Nj+1 for j=1,…,m with Nm+1=N1=N. Explicit limit of empirical eigenvalue distribution of AN(m) is obtained in almost sure convergence as N goes to infinity. In particular, a rich feature of the limiting distributions is presented as the ratio Nj/N fluctuates for each j.

Suggested Citation

  • Zeng, Xingyuan, 2017. "Limiting empirical distribution for eigenvalues of products of random rectangular matrices," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 33-40.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:33-40
    DOI: 10.1016/j.spl.2017.02.025
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    References listed on IDEAS

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    1. J. P. Bouchaud & M. Potters, 2009. "Financial Applications of Random Matrix Theory: a short review," Papers 0910.1205, arXiv.org.
    2. J.-P. Bouchaud & L. Laloux & M. A. Miceli & M. Potters, 2007. "Large dimension forecasting models and random singular value spectra," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 201-207, January.
    3. Giacomo Livan & Luca Rebecchi, 2012. "Asymmetric correlation matrices: an analysis of financial data," Papers 1201.6535, arXiv.org, revised Apr 2012.
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    Cited by:

    1. Yongcheng Qi & Mengzi Xie, 2020. "Spectral Radii of Products of Random Rectangular Matrices," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2185-2212, December.

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