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arXiv · 0801.2112

Bounds on the Poincare constant under negative dependence

Fraser Daly·Oliver Johnson
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Abstract

We give bounds on the Poincare (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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Fraser Daly, Oliver Johnson. 2012-11-05. Bounds on the Poincare constant under negative dependence. https://arxiv.org/abs/0801.2112

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