I'm starting to work in random walks and I have two big questions I would like to have suggestions about.
(1) Consider a system of N point particles undergoing Brownian motion (random walks) on a 3D space with equal diffusion coefficients D and an average spacing L. If we have a probability p of these particles merging when they are found at a distance [d1,d2], how many particles will we have after a time t?
(2) Consider a system of two point particles undergoing random walks BUT confined to a sphere of radius a each, which intersect in some section. How can we estimate their first passage time - that is, the time at which they would be found at a distance [d1,d2]?
Since now thanks for any ideas or suggestions or for pointing me to articles!! The guys in physics stackexchange were all like "this is homework" (wtf???!!!)