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Math Help - Two-dimensional random walk

  1. #1
    Newbie
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    Jun 2008
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    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:

     <br />
\dfrac{1}{2|x|}<br />

    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
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  2. #2
    Super Member
    Joined
    Apr 2009
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    @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
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