Suppose we have a matrix $A \in \mathbb{R}^{n\times n}$ where

$$A_{ij} = \begin{cases} 1 & \text{with probability} \quad p\\ 0 &\text{with probability} \quad1-p\end{cases}$$

I would like to know the following expected value

$$\lim_{n \rightarrow \infty} \mathbb E(| \det (A) |)$$

i.e., the asymptotic behavior as $n$ becomes large.

###What I tried so far

It feels like this has been done already, but after searching for quite a while I performed simulations and it looks like

$$\mathbb E(|\det(A)|) \propto e^{N f(p) }$$

where $f$ is some function of the probability $p$.

$E(|det A|)$ over $n$ for $p=0.5$ were the average is taken over 100 realizations" />

I would be very happy if someone knows the result or a good reference where I could look it up.