Imagine three identical particles, each having the same radius and diffusion constant. The particles diffuse isotropically in 2d or 3d space and each of their concentrations as a function of space and time satisfy the diffusion equation.
When two of the three particles meet, one of them is annihilated and the other keeps diffusing.
Are there any exact mathematical results known about the survival probability for one of these particles given that they all diffuse in either 2d or 3d space?
The survival probability is defined as the probability that a single particle has not yet been annihilated by time t.
Any leads to books, articles, or other information about the solution of this problem would be greatly appreciated.
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