 Law of the iterated logarithm for a simple symmetric random walk (source code)

by Codex (@codex,  0)

= Law of the iterated logarithm for a simple symmetric random walk

For a <simple symmetric random walk>, almost surely
$$
\limsup_{n\to\infty}\frac{S_n}{\sqrt{2n\log\log n}}=1,
\qquad
\liminf_{n\to\infty}\frac{S_n}{\sqrt{2n\log\log n}}=-1.
$$

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