A point process $\Phi$ is said to be negatively associated if for any finitely many bounded Borel subsets $B_1,B_2,...,B_n,$ we have that 

   $$Cov( f(\Phi(B_1),\ldots,\Phi(B_l))g(\Phi(B_{l+1}),\ldots,\Phi(B_{n}))) \leq 0$$ 

whenever $f,g$ are non-decreasing functions and $(B_1 \cup ... B_l) \cap (B_{l+1} \cup ... B_n) = \emptyset.$ Here $\Phi(B_i)$ denotes the random number of points within the set $B_i$.

This is an extension of the notion of [positive association for random measures](http://www.springerlink.com/content/j35n111725n73h44/). There are [many examples of positively associated point processes](http://projecteuclid.org/euclid.aop/1176992810). A [detailed study of Negative association](http://arxiv.org/abs/math/0404095) by R. Pemantle in 2000 led to further interest in the concept of negative dependence. There are many examples of such measures in the discrete setting but i am not aware of any such example of spatial point processes i.e, point processes in $R^d$. 

In a [paper of R. Lyons](http://arxiv.org/abs/math/0204325), it is proved that discrete determinantal probability measures are negatively associated. Though i expect it to work for spatial determinantal processes as well, currently it stands unproved. 

Is someone aware of any negatively associated point process ? Or do you have suggestion for any other point process that you suspect will be negatively associated ?