Fluctuations for annihilations of Brownian spheres (Q1332321)

Consider \(N\) spheres in \(\mathbb{R}^ d\) of radius \(r_ N\) whose centers perform independent Brownian motions. When any two of these spheres collide, they annihilate each other. Record the time and place of each annihilation. The author analyses the system as \(N \to \infty\) and \(Nr_ N \to 0\). If \(N^ 2 r_ N \to\) a limit (nonzero), a Poisson process results, whereas if \(N^ 2r_ N \to \infty\), a Gaussian limit is obtained.