Zhang Yuan quickly established a mathematical model, "Consider the Milky Way as a simple plane, that is, R^2. Contemplate a spaceship performing a standard Brownian motion or two spaceships performing independent standard Brownian motions each.
"When the distance between the two spaceships is less than a certain small constant, for example, 0.01, they are deemed to have encountered each other."
"Since two-dimensional Brownian motion is recurrent in the neighborhood, given enough time, the two spaceships are bound to meet."
"Consider two independent standard Brownian motions A(t), B(t). A(1)+B(1) has the same distribution as A(2), because B(2)=B(1)+[B(2)-B(1)], which is also the sum of two independent standard normal distributions. This means that the sum of two independent standard Brownian motions at time t has the same distribution as a single standard Brownian motion at 2t."
