Probability of pr .: expected determinant of random symmetric matrix with different Gaussian distributions of the diagonal and non-diagonal elements

Consider a random matrix $ A in mathbb {R} ^ {N times N} $ Where the elements are random Gaussian variables. The mean and the variance of the elements are different on the diagonal and on the diagonal:

$ begin {align}
Y= p & text {y} & text {var} (A_ {ij}) = frac {1} {N} p (1-p) & text {if} , i = j \
Y= p ^ 2 & text {y} & text {var} (A_ {ij}) = frac {1} {N} p ^ 2 (1-p ^ 2) & text {if} , i neq j
end {align} $

where $ p in (0.1) $ It is a fixed paremeter. The matrix is ​​symmetric. $ A_ {ij} = A_ {ji} $.

Now I would like to know

$ begin {align}
mathbb {E}[lim_{Nrightarrow infty} |det A|],
end {align} $

that is, the asymptotic behavior as $ N $ It becomes big. Since the variations approach zero for $ N rightarrow infty $ I suppose that the expectation of the absolute value of the determinant also approaches zero.

Is there a method to determine this behavior or does someone know how to do it?