Related papers: Interevent time distribution in seismicity: a theo…
The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The…
Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade…
We study earthquake interval time statistics, paying special attention to inter-occurrence times in the two-dimensional (2D) stick-slip (block-slider) model. Inter-occurrence times are the time interval between successive earthquakes on all…
Interevent times have been studied across various disciplines in search for correlations. In this paper we show analytical and numerical evidence that at the population level a power-law can be obtained by assuming poissonian agents with…
The statistics of recurrence times in broad areas have been reported to obey universal scaling laws, both for single homogeneous regions (Corral, 2003) and when averaged over multiple regions (Bak et al.,2002). These unified scaling laws…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
We explore in depth the validity of a recently proposed scaling law for earthquake interevent time distributions in the case of the Southern California, using the waveform cross-correlation catalog of Shearer et al. Two statistical tests…
We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. We study the probability density function (PDF) $P(t_{\rm m}|T)$ of the time $t_{\rm m}$ at which $x(\tau)$ reaches its global maximum. By using a path…
Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus…
The statistical properties of the seismic time series data in southern California are studies. In particular, the calm time intervals, which are the time intervals between successive significant earthquakes above the fixed threshold value…
Recently Osorio et al (Eur. J. Neurosci., 30 (2009) 1554) reported that probability distribution of intervals between successive epileptic seizures follows a power law with exponent 1.5. We theoretically explain this finding by modeling…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
After a large earthquake, the likelihood of successive strong aftershocks needs to be estimated. Exploiting similarities with critical phenomena, we introduce a scaling law for the decay in time following a main shock of the expected number…
We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the…
Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality,…
The waiting time distribution $w(\tau)$, i.e. the probability for a delay $\tau$ between two subsequent transition (`jumps') of particles, is a statistical tool in (quantum) transport. Using generalized Master equations for systems coupled…
We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with…
Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record…
We introduce an index based on information theory to quantify the stationarity of a stochastic process.The index compares on the one hand the information contained in the increment at the time scale $\tau$ of the process at time $t$ with,…