# Entropic CLT and phase transition in high-dimensional Wishart matrices

@article{Bubeck2015EntropicCA, title={Entropic CLT and phase transition in high-dimensional Wishart matrices}, author={S{\'e}bastien Bubeck and Shirshendu Ganguly}, journal={ArXiv}, year={2015}, volume={abs/1509.03258} }

We consider high dimensional Wishart matrices $\mathbb{X} \mathbb{X}^{\top}$ where the entries of $\mathbb{X} \in {\mathbb{R}^{n \times d}}$ are i.i.d. from a log-concave distribution. We prove an information theoretic phase transition: such matrices are close in total variation distance to the corresponding Gaussian ensemble if and only if $d$ is much larger than $n^3$. Our proof is entropy-based, making use of the chain rule for relative entropy along with the recursive structure in the…

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