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We discuss intermittent time series consisting of discrete bursts or avalanches separated by waiting or silent times. The short time correlations can be understood to follow from the properties of individual avalanches, while longer time…
Self-organized criticality has been claimed to play an important role in many natural and social systems. In the present work we empirically investigate the relevance of this theory to stock-market dynamics. Avalanches in stock-market…
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…
There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
We present in this article an analysis of some of the properties of the density field realized in numerical simulations for power-law initial power-spectra in the case of a critical density universe. We compare our numerical results in the…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
We discuss some applications of the Mittag-Leffler function and related probability distributions in the theory of renewal processes and continuous time random walks. In particular we show the asymptotic (long time) equivalence of a generic…
Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The…
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…
The scalability of massively parallel algorithms is a fundamental question in computer science. We study the scalability and the efficiency of a conservative massively parallel algorithm for discrete-event simulations where the discrete…
This paper introduces a discrete-time fractional Poisson process defined as a renewal process, where the waiting times follow a discrete Mittag-Leffler distribution. We investigate its fundamental properties by explicitly deriving the…
We explore the finite dimensional distributions of the second-order scattering transform of a class of non-Gaussian processes when all the scaling parameters go to infinity simultaneously. For frequently used wavelets, we find a coupling…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
In the framework of the Statistical Multifragmentation Model, the nuclear isoscaling analysis is extended to constrain the ratio between the sizes of the decaying sources formed in a collision between two heavy ions. It is found that the…