In [1] Dubhashi, Jonasson, and Ranjan study the negative dependence properties of Srinivasan’s sampling processes (SSPs), random processes which sample sets of a fixed size with prescribed marginals. In particular they prove that linear SSPs have conditional negative association, by using the Feder-Mihail theorem [3] and a coupling argument. We consider a broader class of SSPs that we call tour...

The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of positively dependent events. There is, as yet, no corresponding theory of negatively dependent events. There is, however, a need for such a theory. This paper, ...

In [1] Dubhashi, Jonasson, and Ranjan study the negative dependence properties of Srinivasan’s sampling processes (SSPs), random processes which sample sets of a fixed size with prescribed marginals. In particular they prove that linear SSPs have conditional negative association, by using the Feder-Mihail theorem [3] and a coupling argument. We consider a broader class of SSPs that we call tour...

We show how the FKG Inequality can be used to prove negative dependence properties.

We introduce the class of strongly Rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class contains e.g. product measures, uniform random spanning tree measures, and large classes of determinantal probability measures and distributions for symmetric exclusion processes. We show that strongly Rayleigh m...

Conspecific negative density-dependent establishment, in which local abundance negatively affects establishment of conspecific seedlings through host-specific enemies, can influence species diversity of plant communities, but the generality of this process is not well understood. We tested the strength of density dependence using the United States Forest Service's Forest Inventory and Analysis ...