A Closer Look at The Fine Structure of The Random Walk on (0,1)

Abstract

Let $S_n$ be the random walk on $(0,1)$. The $S_n$ have been the subject of intense study; their definition is immediately intuitive. Nevertheless, they are quite intentionally disorderly, and this disorder is mirrored by the fact that, pointwise, $(\frac{S_n}{\sqrt{n}}\mid n\in {\mathbb{N}}^{+})$ behaves quite badly.

In this paper, we provide our results on the fine structure of the random walk that give insight into this behavior.