Bounds on the Poincare constant under negative dependence
Probability
2013-03-20 v2
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.
Cite
@article{arxiv.0801.2112,
title = {Bounds on the Poincare constant under negative dependence},
author = {Fraser Daly and Oliver Johnson},
journal= {arXiv preprint arXiv:0801.2112},
year = {2013}
}