Positive Influence and Negative Dependence

Authors:
Devdatt Dubhashi;Johan Jonasson;Desh Ranjan
Affiliations:
Department of Computing Science, Chalmers University of Technology, SE 412 96 Göteborg, Sweden (e-mail: dubhasi@cs.chalmers.se);Department of Mathematics, Chalmers University of Technoloy, SE 412 96 Göteborg, Sweden (e-mail: jonasson@math.chalmers.se);Department of Computer Science, New Mexico State University, Las Cruces, New Mexico 88003, USA (e-mail: dranjan@cs.nmsu.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2007

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Negative dependence and srinivasan's sampling process

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Abstract

We study negative dependence properties of a sampling process due to Srinivasan to produce distributions on level sets with given marginals. We give a simple proof that the distribution satisfies negative association. We also show that under a linear match schedule it satisfies the stronger condition of conditional negative association via a non-trivial application of the Feder–Mihail theorem. This method involves the notion of a variable of positive influence. We give some results and related counter-examples which might shed some light on its role in a theory of negative dependence.