English

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.

Keywords

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}
}
R2 v1 2026-06-21T10:02:44.813Z