Dominating random variable of $1/\lambda_{\min}(X^\top X/n)$

Question

Let $Y_{n,p} = \frac{1}{\lambda_{\min}(X_{n,p}^\top X_{n,p}/n)}$ be a sequence of random variables, where all entries of $X_{n,p}\in \mathbb{R}^{p\times n}$ are i.i.d. standard normal. We will let $n,p\to \infty$ with $n/p\to y\in (0,1)$. Is there a dominating random variable for $Y_{n,p}$ (i.e., an integrable random variable $Z$ such that $|Y_{n,p}|\le Z$)?