Bounds on the Poincaré constant under negative dependence

Fraser Daly and Oliver Johnson

Statistics & Probability Letters, 2013, vol. 83, issue 2, 511-518

Abstract: 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.

Keywords: Poincaré constant; Total negative dependence; Ultra log-concavity; Size-bias transform; Stochastic ordering (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2012.11.001

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