Random (drankard) walk distance after n steps

[MrRoth]

i am tying to analyze a random walk on an integer lattice $\mathbb{Z}^k$. for $k=1$, what is the probability that after steps the drunkard's distance from the origin is lower than $\sqrt{n}$?

 

[kai_sikorski]

People on math overflow already gave you a good reference. This is a direct application of the central limit theorem.

 

[MrRoth]

i need someone to elaborate on the topic. not to give me an answer. i.e. how was the parameters and the model derived.