A Simple Alternative

Instead of taking the square of the difference, the first order correlation can be used directly to give:

$${\sigma_x}^2 = \frac{- d^{\, 2}}{4 \ln\left( \frac{E \{ F_S(... ...remath{\mathbf{x}}) F_S(\ensuremath{\mathbf{x}}) \} } \right)}$$ (49)