I have two sets of n0 events each generated independently by an exponential distribution with characteristic time tau (dn/dt = n0/tau exp(-t/tau)). What is the probability that there will be no coincidences between the two sets, ie no time window of duration T with at least one event from each set ? Intuitively, the probability is a function of x=tau/n0 /T that goes to 1 for x=0 to 0 for large x, but I need a precise form for the function - if one exists.