Let $X = (x_{ij}) \in \mathbb{R}^{n \times p}$ be a matrix with independent $N(0,1)$ entries.
We know that $\max_j x_{ij} < \sqrt{2\log(p/\delta)}$ with probability at least $1-\delta$.
I would like to obtain a lower bound for $\min_i (\max_j x_{ij})$ that holds with probability at least $1-\delta$. Could somebody point to a relevant reference please?