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On the dependence structure of negatively dependent measures
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Descriptif
A major breakthrough in the theory of negatively dependent – i.e., repulsive – probability measures was the introduction of “strongly Rayleigh measures” by Borcea, Brändén and Liggett in 2009. These measures constitute a very well-behaved and rich class of probability measures, so much so that they are considered the “main” class of negatively dependent measures. An interesting feature of negatively dependent measures is their complex dependence structure. This is essentially due to intrinsic constraints in their dependence structure. In this talk, I will present two strong manifestations of this phenomenon in the class of strongly Rayleigh measures: (i) tail triviality, which is equivalent to asymptotic independence of distant parts of the stochastic process, and (ii) paving property, which, roughly speaking, says that it is possible to partition a set of strongly Rayleigh random variables into a small number of subsets such that the random variables in each subset are “almost independent”. This talk is based on joint works with Kasra Alishahi and Mohammadsadegh Zamani.
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