• Corpus ID: 248986539

# \$XX^T\$ Matrices With Independent Entries

```@inproceedings{Bose2022XXTMW,
title={\\$XX^T\\$ Matrices With Independent Entries},
author={Arup Bose and Priyanka Sen},
year={2022}
}```
• Published 22 May 2022
• Mathematics
Let S = XX T be the (unscaled) sample covariance matrix where X is a real p × n matrix with independent entries. It is well known that if the entries of X are independent and identically distributed (i.i.d.) with enough moments and p / n → y (cid:44) 0, then the limiting spectral distribution (LSD) of 1 n S converges to a Marˇcenko-Pastur law. Several extensions of this result are also known. We prove a general result on the existence of the LSD of S in probability or almost surely, and in…

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