Residence Time Statistics for N Renewal Processes

We present a study of residence time statistics for N renewal processes with a long tailed distribution of the waiting time. Such processes describe many nonequilibrium systems ranging from the intensity of N blinking quantum dots to the residence time of N Brownian particles. With numerical simulations and exact calculations, we show sharp transitions for a critical number of degrees of freedom N. In contrast to the expectation, the fluctuations in the limit of N -> infinity are nontrivial. We briefly discuss how our approach can be used to detect nonergodic kinetics from the measurements of many blinking chromophores, without the need to reach the single molecule limit.