Towards a theory of negative dependence

Details Towards a theory of negative dependence Towards a theory of negative dependence

2004-04-05

arxiv.org/abs/math/0404095v1

J. Math. Phys., 41, 1371 - 1390 (2000)

Mathematics

Probability

31 pages

Scientific paper

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, unfortunately, contains no substantial theorems. Its purpose is to present examples that motivate a need for such a theory, give plausibility arguments for the existence of such a theory, outline a few possible directions such a theory might take, and state a number of specific conjectures which pertain to the examples and to a wish list of theorems.

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