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In a scenario where there are two people in the rooms next to each other randomly walking in a room I want to know if we can compute PDF of distance between the two people. So the way I tried to tackle the problem is to reduce it to one person standing still and other person walking and trying to formulate the PDF but I still couldnt work out how to assign the PDF.

Say that the rooms form a square shape $AxA$ and one person is standing still and other randomly walking. I would like to know what would the distribution will look like for the distance between two people if one person is stationary in the center as shown and other person is doing random walk. Given the maximum possible distance between the two people is $dmax$ and minimum possible distance is $dmin$

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GENIVI-LEARNER
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    This is not solvable without more information about these "random walks:" what is the distribution of locations of an individual and how are the two random walks related? Would you perhaps be trying to ask this question: https://stats.stackexchange.com/questions/52909 ? – whuber Oct 20 '20 at 20:56
  • @whuber Noted, what I assumed that these random walks follow brownian motion and parameters for those are arbitrary, the distribution is uniform across the room, the two random walks are independent of each other. Let me review your reference and get back. What I feel quite daunting is how to assign the distribution in continuous space as measure can only be assigned to a subset. – GENIVI-LEARNER Oct 20 '20 at 21:03
  • @whuber I shall revise the question after reading your reference. – GENIVI-LEARNER Oct 20 '20 at 21:06
  • You will need to describe what you mean by Brownian Motion confined to a rectangle. The attempt to do that is likely to suggest ways to attack you problem, too. – whuber Oct 20 '20 at 22:51

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