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 D, and sampling n times from it.
Denote by X1,…,Xn the corresponding random variables, with the following dependency:
Once having sampled Xi, it is not possible any more to get another sample "close" to it any more, or in other words,
∃δ>0,∀i≠j,|Xi−Xj|≥δ