Distribution of the largest eigenvalue of a sample covariance matrix (Bernoulli distribution sample)

Question

Given a sample matrix $\mathbf{X} \in \mathbb{C}^{p\times n}$, whose entry follow i.i.d bernoulli distribution (The probability of the value being either $+1$ or $-1$ is $\frac{1}{2}$). When $p$ is fixed, and $n \to \infty$, what is the distribution of the maximum eigenvalue of $S=XX^T$? Are there any related studies?