# Math Help - Two-dimensional random walk

1. ## Two-dimensional random walk

Hello

Suposse we have a particle in the plane at the origin $(0,0).$

It moves randomly on the integer lattice $Z^2$ to any of the adjacent vertex with equal probability $1/4$.

The question is what's the probabiliy of reach a fixed point $(x,y)$ before return to the origin?

The analog problem in one dimension is easy. Such probability is:

$
\dfrac{1}{2|x|}
$

I have read some related articles working on finite graphs; but I am not be able to obtain the answer for my problem.

Thank you very much for your attention

2. @el_manco - Hi - This has been troubling me since you posted this.

Infact I am not even to able to prove your point about 1-D random walk.

Can anyone help me with the 1-D problem?

And any insights about 2-D problem