Asymptotic behavior of the geometric(p) rainstick as p --> 0
Year: 2017
Type: preprint
Abstract: In the geometric($p$) rainstick process, raindrops fall one at a time on the positive integers, landing at $k$ with probability $(1-p)^{k-1}p$. Let $N$ be the first time that for some $K$ all sites in $[1,K]$ are wet and all sites in $(K,\infty)$ are dry. We will prove results that describe the asymptotic behavior as $p\to 0$. We invite the reader to guess the answer before it is revealed below.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2790883461