Real world application to theoretical sampling process

Question

Does the following sampling process have any particular application/meaning in physics ? Does it correspond to some real world sampling process ?

Consider an arbitrary probability distribution $\mathcal{D}$, and sampling $n$ times from it. 
Denote by $X_1, \dots, X_n$ the corresponding random variables, with the following dependency:
Once having sampled $X_i$, it is not possible any more to get another sample "close" to it any more, or in other words,

$$\exists \delta > 0, \forall i \neq j, |X_i - X_j| \geq \delta$$

Comments

sounds like hard-core models in statistical mechanics to me.