Hello, my question basically is how do I find the probability density function of the position of the nodes in a given area after N discrete time slots when the nodes move following the 2D random walk model.
In case the question isn't clear, I'll just explain again. say I'm generating 50 nodes from Uniform distribution in a circular area of radius D. The initial positions(r,$\theta$) of these nodes have been generated as follows : $r$ ~Unif[0,D] and $\theta$~Unif($-\pi,\pi$]. Then each of these nodes pick up a random direction of motion in the range $\phi$~Unif($-\pi,\pi$]. I want to know the distribution of the positions of these nodes after a long time, say T time slots. Each of these time slots are of fixed length and every node moves with a fixed velocity $v$ in every time slot. Can someone help me on this? It seemed to be quite a basic problem and the solution to this should exist in the literature, may be in some other context, but I couldn't find any.