  Given a wave-function minimizing the Levy-Lieb functional, the intent of this
short note is to give an estimate of the probability of the particles being in
positions $(x_1, \ldots, x_N)$ in the $\delta$-close regime $D_{\delta}=
\cup_{i \neq j} \{|x_i - x_j| \leq \delta\}$.
