Distribution of Return Periods of Rare Events in Correlated Time Series

We study the effect on the distribution of return periods of rare events of the presence in a time series of finite‐term correlations with non‐exponential decay. Precisely, we analyze the auto‐correlation function and the statistics of the return intervals of extreme values of the resistance fluctuations displayed by a resistor with granular structure in a nonequilibrium stationary state. The resistance fluctuations, δR, are calculated by Monte Carlo simulations using the SBRN model introduced some years ago by Pennetta, Trefan and Reggiani and based on a resistor network approach. A rare event occurs when δR overcomes a threshold value q significantly higher than the average value of the resistance. We have found that for highly disordered networks, when the auto‐correlation function displays a non‐exponential decay but yet the resistance fluctuations are characterized by a finite correlation time, the distribution of return intervals of the extreme values is well described by a stretched exponential, wi...