ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5430 on D3360: Standard integer random walk
Growth rate for the expectation of the absolute value of the standard integer random walk
Formulation 0
Let $S : \mathbb{N} \to \text{Random} (\mathbb{Z})$ be the D3360: Standard integer random walk.
Then \begin{equation} \lim_{N \to \infty} \frac{\mathbb{E} |S_N|}{\sqrt{N}} = \sqrt{\frac{2}{\pi}} \end{equation}