Is it possible to find the expectation value of the following object analytically?
$F(u_1,u_2,\ldots,u_N)=\prod_{i=1}^{N}(1-\alpha(u_i-u_{i-1})^2)$, where $u_{0}\equiv 0$. $u_i$'s are independent and identically distributed random variables from the uniform distribution $[-w/2,w/2]$.