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We study the behavior of several joint residence times of N independentBrownian particles in a disc of radius $R$ in two dimensions. We consider: (i)the time T_N(t) spent by all N particles simultaneously in the disc within thetime interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of Nparticles spend together in the disc within the time interval [0,t]; and (iii)the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spendtogether in the disc within the time interval [0,t]. We obtain very simpleexact expressions for the expectations of these three residence times in thelimit t\to\infty.Comment: 8 page

On the joint residence time ofNindependent two-dimensional Brownian motions