ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5430 on D3360: Standard integer random walk
Subresult of R5436:

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}

Also known as

Growth rate for the expected distance of the standard integer random walk from the origin

Subresults

▶	R5431: Growth class for the expectation of the absolute value of the standard integer random walk