Bounds on the Poincaré constant under negative dependence
We give bounds on the Poincaré (inverse spectral gap) constant of a non-negative, integer-valued random variable W, under negative dependence assumptions such as ultra log-concavity and total negative dependence. We show that the bounds obtained compare well to others in the literature. Examples treated include some occupancy and urn models, a random graph model and small spacings on the circumference of a circle. Applications to Poisson convergence theorems are considered.
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Volume (Year): 83 (2013)
Issue (Month): 2 ()
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