Abstract
For positive integers $s, n$ let $M_s = (1/s)V_sV^T_s$, where $V_s$ is an $n \times s$ matrix composed of i.i.d. $N(0, 1)$ random variables. Assume $n = n(s)$ and $n/s \rightarrow y \in (0, 1)$ as $s \rightarrow \infty$. Then it is shown that the smallest eigenvalue of $M_s$ converges almost surely to $(1 - \sqrt y)^2$ as $s \rightarrow \infty$.
Citation
Jack W. Silverstein. "The Smallest Eigenvalue of a Large Dimensional Wishart Matrix." Ann. Probab. 13 (4) 1364 - 1368, November, 1985. https://doi.org/10.1214/aop/1176992819
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