Related papers: Point-occurrence self-similarity in crackling-nois…
A symmetric random walk $X$ whose jumps have diffuse law, looked at up to an independent geometric random time, splits at the minimum into two independent and identically distributed pieces. The same for the maximum. It is natural to ask,…
It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the…
An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…
Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the…
Acoustic emission or crackling noise is measured from an experiment on splitting or peeling of paper. The energy of the events follows a power-law, with an exponent $\beta \sim 1.8\pm 0.2$. The event intervals have a wide range, but…
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…
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…
We show that a scaling law exists for the near resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasi-classical phase-space representation of the quantum system with noise…
In this study we aim for a deeper understanding of the power law slope, $\alpha$, of waiting time distributions. Statistically independent events with linear behavior can be characterized by binomial, Gaussian, exponential, or Poissonian…
We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized…
For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have reveals that this anomalous scaling causes a…
The self-similarity in space and time (hereafter self-similarity), either deterministic or statistical, is characterized by similarity exponents and a function of scaled variable, called the scaling function. In the present paper, we…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
Many systems in nature are conjectured to exist at a critical point, including the brain and earthquake faults. The primary reason for this conjecture is that the distribution of clusters (avalanches of firing neurons in the brain or…
An accurate understanding of the interplay between random and deterministic processes in generating extreme events is of critical importance in many fields, from forecasting extreme meteorological events to the catastrophic failure of…
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…