have we "random walk" specialist here?
I want proof
$\lim_{n\to\infty}\mathbb{P}\left(S_n>\sqrt n log(n)\right)=0$
$\lim_{n\to\infty}\mathbb{P}\left(|S_n|>\frac{\sqrt(n)}{log(n)}\right)=1$ that, which $S_n,$$_{\mathbb{N}}\in \mathbb{N_0}$ is a simple random walk.
My Ideas: I want use the central limit theorem for that i need expectation and the variance. The transform is difficult for me.