Universal diagonal estimates for minimizers of the Levy-Lieb functional

Abstract

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 $D_{\delta}= \cup_{i \neq j} \{|x_i - x_j| \leq \delta\}$.