离散游程高度分布
组合数学
2012-08-14 v2
摘要
我们计算了步长集由一个正步长 1 和任意有限个非正整数组成的随机离散游程高度的极限分布。该极限律是 Brown 游程的上确界。这对于 Dyck 路径和 Motzkin 路径而言是众所周知的。我们应用了 Bousquet-Melout 在 2008 年的一篇论文中提出的关于长度和高度生成函数的某种 Schur 多项式表示，这导出了易于进行 Mellin 变换分析的矩生成函数形式。
引用
@article{arxiv.1208.1367,
title = {The Distribution of Heights of Discrete Excursions},
author = {Uwe Schwerdtfeger},
journal= {arXiv preprint arXiv:1208.1367},
year = {2012}
}
备注
This paper has been withdrawn by the author due to an error in section 2.3. Unless a=1, more than the said k+1 tableaux have to be taken into account. As it stands the subsequent derivation is only valid for a=1, i.e. excursions with precisely one positive step 1 and an arbitrary finite set of non-positive steps