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The so-called chaotic states that emerge on the model of $XY$ interacting on regular critical range networks are analyzed. Typical time scales are extracted from the time series analysis of the global magnetization. The large spectrum…
We present results from a physical experiment which demonstrates that a sheared granular medium behaves in a manner analogous to earthquake activity. The device consists of an annular plate rotating over a granular medium in a stick-slip…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we provide a deeper understanding of these intricate limiting…
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in…
We analyze the waiting time distribution of time distances $\tau$ between two nearest-neighbor flares. This analysis is based on the joint use of two distinct techniques. The first is the direct evaluation of the distribution function…
We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar…
We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed…
We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global…
The location of the unique supremum of a stationary process on an interval does not need to be uniformly distributed over that interval. We describe all possible distributions of the supremum location for a broad class of such stationary…
Enduring violent conflicts are interrupted by lulls without violence. Studies of interevent times found power law distributions based on coarse-grained data with a resolution of one day. Fine-grained data of violence with a resolution of…
Quantitative understanding of human behaviors provides elementary comprehension of the complexity of many human-initiated systems. A basic assumption embedded in the previous analyses on human dynamics is that its temporal statistics are…
The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event.…
Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occuring during a given time. Time-based approaches use the statistics of the time needed to reach a given number of…
The distribution of the return intervals $\tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined…
We report a similarity of fluctuations in equilibrium critical phenomena and non-equilibrium systems, which is based on the concept of natural time. The world-wide seismicity as well as that of San Andreas fault system and Japan are…
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the nontrivial dynamics of the…
We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…
Several works have observed heavy-tailed behavior in the distributions of returns in different markets, which are observable indicators of underlying complex dynamics. Such prior works study return distributions that are marginalized across…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…