有界尺寸偏耦合、对数凹分布及占据模型的测度集中
概率论
2017-05-25 v3 统计理论
统计理论
摘要
基于具有对数凹边缘分布的多变量占据模型的阈值型计数，在弱条件下允许有界尺寸偏耦合，从而为随机图、随机几何中的 germ-grain 模型、多项式分配模型以及多变量超几何抽样导出了新的测度集中结果。该工作在多个方向上推广并改进了先前的结果。
引用
@article{arxiv.1402.6769,
title = {Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models},
author = {Jay Bartroff and Larry Goldstein and Ümit Işlak},
journal= {arXiv preprint arXiv:1402.6769},
year = {2017}
}
备注
35 pages. Version 2 is the result of a major revision, including corrections and significant clarifications in particular as regards Lemmas 2.6 and 2.7, and the introduction and use of Property (B,*) in Definition 2.2. Version 3 added some references and removed Theorem 1.1