On spectrum of sample covariance matrices from large tensor vectors
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913188018126848 |
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| author | Yuan, Wangjun |
| author_facet | Yuan, Wangjun |
| contents | In this paper, we investigate the limiting empirical spectral distribution (LSD) of sums of independent rank-one $k$-fold tensor products of $n$-dimensional vectors as $k,n \to \infty$. Assuming that the base vectors are complex random variables with unit modular, we show that the LSD is the Marčenko-Pastur law. Comparing with the existing results, our limiting setting allows $k$ to grow much faster than $n$. Consequently, we obtain the necessary and sufficient conditions for Marčenko-Pastur law to serve as the LSD of our matrix model. Our approach is based on the moment method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05834 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On spectrum of sample covariance matrices from large tensor vectors Yuan, Wangjun Probability In this paper, we investigate the limiting empirical spectral distribution (LSD) of sums of independent rank-one $k$-fold tensor products of $n$-dimensional vectors as $k,n \to \infty$. Assuming that the base vectors are complex random variables with unit modular, we show that the LSD is the Marčenko-Pastur law. Comparing with the existing results, our limiting setting allows $k$ to grow much faster than $n$. Consequently, we obtain the necessary and sufficient conditions for Marčenko-Pastur law to serve as the LSD of our matrix model. Our approach is based on the moment method. |
| title | On spectrum of sample covariance matrices from large tensor vectors |
| topic | Probability |
| url | https://arxiv.org/abs/2306.05834 |