Eigenvalue Distributions of Sums and Products of Large Random Matrices via Incremental Matrix Expansions
<|reference_start|>Eigenvalue Distributions of Sums and Products of Large Random Matrices via Incremental Matrix Expansions: This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using R- and S-transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser CDMA system with a minimum mean-square error linear receiver.<|reference_end|>
@article{peacock2005eigenvalue,
    title={Eigenvalue Distributions of Sums and Products of Large Random Matrices
  via Incremental Matrix Expansions},
    author={Matthew J.M. Peacock, Iain B. Collings, Michael L. Honig},
    journal={arXiv preprint arXiv:cs/0511054},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0511054},
    primaryClass={cs.IT math.IT}
}