Abstract
We study the limiting spectral distribution of large-dimensional sample covariance matrices associated with the order-d symmetric random tensors formed by products of d variables chosen from n independent standardized random variables. We find optimal sufficient conditions for this distribution to be the Marchenko-Pastur law in the case and . Our conditions reduce to when the variables have uniformly bounded fourth moments. The proofs are based on a new concentration inequality for quadratic forms in symmetric random tensors and a law of large numbers for elementary symmetric random polynomials.
Funding Statement
This work was supported by the Russian Science Foundation under grant no. 18-71-10097, https://www.rscf.ru/project/18-71-10097/, https://rscf.ru/project/21-71-03017/.
Acknowledgments
The author would like to thank an anonymous referee for his/her valuable comments that greatly improved the paper.
Citation
Pavel Yaskov. "Marchenko-Pastur law for a random tensor model." Electron. Commun. Probab. 28 1 - 17, 2023. https://doi.org/10.1214/23-ECP527
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