Related papers: Point-occurrence self-similarity in crackling-nois…

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…

Statistical similarities between earthquakes and other systems that emit cracking noises have been explored in diverse contexts, ranging from materials science to financial and social systems. Such analogies give promise of a unified and…

Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…

The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…

It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk…

Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…

Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of…

We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…

For many driven-nonequilibrium systems, the probability distribution functions of magnitude and recurrence-time of large events follow a powerlaw indicating a strong temporal correlation. In this paper we argue why these probability…

We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $\pi = \{x_0,…

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate…

The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…

Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined…

We study scaling limits of non-increasing Markov chains with values in the set of non-negative integers, under the assumption that the large jump events are rare and happen at rates that behave like a negative power of the current state. We…

Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of oriented percolation involve very nonlinear…

When far from equilibrium, many-body systems display behavior that strongly depends on the initial conditions. A characteristic such example is the phenomenon of plasticity of crystalline and amorphous materials that strongly depends on the…

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not…

We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…