论 (0,∞) 上尺度不变泊松过程的核心作用
概率论
2016-11-18 v1
摘要
(0,∞) 上的尺度不变泊松过程在数论、组合学和遗传学中扮演着核心但略显隐蔽的角色。它们给出了连续极限，这些极限构成并统一了多种离散结构，包括均匀选取整数的素因子分解、有限域上多项式的因式分解、随机排列的循环分解、随机映射的分支分解以及 Ewens 抽样公式。它们作为概率论的基本和核心对象之一，值得关注。
引用
@article{arxiv.1611.05572,
title = {On the central role of the scale invariant Poisson processes on (0,infty)},
author = {Richard Arratia},
journal= {arXiv preprint arXiv:1611.05572},
year = {2016}
}
备注
Hyperlink and backref version of the paper which originally was published in {Microsurveys in discrete probability ({P}rinceton, {NJ}, 1997)}, SERIES = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.}, VOLUME = {41}, PAGES = {21--41}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {1998}