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

Growth class 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} \mathbb{E} |S_N| = O(\sqrt{N}) \end{equation}

Proofs

Proof 0

Let $S : \mathbb{N} \to \text{Random} (\mathbb{Z})$ be the D3360: Standard integer random walk.