The determinant magnitude conjecture for random sign matrices

Let $M_n$ be an $n\times n$ random matrix with independent Rademacher entries. Hadamard's inequality gives $|\det M_n|\leq n^{n/2}$.

Determinant magnitude conjecture. Almost surely,

$$|\det M_n|=n^{(1/2-o(1))n}.$$

The source states that Tao and Vu established a matching lower bound, confirming this conjecture, so it is solved.