The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincaré recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series. In particular, we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function, on the interval whereto the recurrences are observed, and on the temporal correlations of time series. In the case of long-term correlations, we verify the validity of the stretched exponential distribution, which is uniquely defined by the exponent $γ$, at the same time showing that it is restricted to the class of linear long-term correlated processes. Simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different $γ$, which shows a lack of invariance under the change of observables.
Recurrence intervals between earthquakes strongly depend on history
本文研究了M $ in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time $ τ_0 $. As a consequence, the conditional mean recurrence time $ \hat τ以上地震复发时间的统计（τ_0）$ between two events increases monotonically with $ τ_0 PDMATHAMQ τ_0 PDMATHAMR PDMATHAMS τ，PDMATHAMO τ（τ_0）$ is smaller than $ \ov τ $, while for $ τ_0> \ov τ $, $ \hat τ（τ_0）$ is greater than $ \ov τ $. Also the mean residual time until the next earthquake does not depend only on the elapsed time, but also strongly on $ τ_0 $. The larger $ τ_0$越大，则平均剩余时间越大。在任何地震预报中，都应考虑上述特征。
Complex network topological and spectral determinants of extreme events
University of Bonn（波恩大学）；Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn（波恩大学赫尔姆霍兹辐射与核物理研究所）；Carl von Ossietzky Universität Oldenburg（奥尔登堡卡尔·冯·奥西茨基大学）
