一个修正的 Poincare 不等式及其在首发渗流中的应用
概率论
2007-05-23 v2
摘要
我们将一个高斯泛函不等式推广到高斯测度的可数积上。该不等式改进了经典的高斯测度 Poincare 不等式。作为一个应用，我们证明当边时分布属于一类广泛的连续分布（包括指数分布）时，首发渗流具有次线性方差。这推广了 Benjamini、Kalai 和 Schramm 关于正 Bernoulli 边时的结果。
关键词
引用
@article{arxiv.math/0602496,
title = {A modified Poincare inequality and its application to First Passage Percolation},
author = {Michel Benaim and Raphael Rossignol},
journal= {arXiv preprint arXiv:math/0602496},
year = {2007}
}
备注
After having completed a first version of this paper, we were informed that our main inequality, which we claimed to be new, was implied by a work of Bobkov and Houdre. See details in the revised paper