The following is the theorem 6.5.1 from Vershynin's High Dimensional Probability theory:
Let $A$ be an $n × n$ symmetric random matrix whose entries on and above the diagonal are independent, mean zero random variables. Then
$$\mathbb E\|A\| \le C \sqrt{\log n} \cdot \mathbb E\max_i(\|A_i\|_2),$$ where $A_i$ are the rows of $A$.
I want to find an example that shows the sharpness of this bound, i.e. find an $A$ satisfying the hypotheses such that
$$\mathbb E\|A\| \ge c \sqrt{\log n} \cdot \mathbb E\max_i(\|A_i\|_2).$$
Note the $c$ could be different from the $C$.
The $\log n$ looks very strange to me and I don't know how to find $A$ to product a factor like that...