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In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While…
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…
Isolated complex networks have been studied deeply in the last decades due to the fact that many real systems can be modeled using these types of structures. However, it is well known that the behavior of a system not only depends on…
In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic departed from those of traditional short range dependent models, and were instead characterized by asymptotic self-similarity. Following this…
The paper assesses stationary probability distributions in out of equilibrium systems. In the phenomenology proposed, no free energy can be well defined. Fluctuations of Landau free energy couplings arise when the intrinsic chemical…
Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…
In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very…
We describe fluctuations in finite-size networks with a complex distribution of connections, $P(k)$. We show that the spectrum of fluctuations of the number of vertices with a given degree is Poissonian. These mesoscopic fluctuations are…
A modification of the Skellam and Poisson distributions is proposed for subsystems when the constraints imposed by the charge conservation law in the complete system are taken into account. Such distributions can be applied, for example,…
We consider a system of $N$ neurons, each spiking randomly with rate depending on its membrane potential. When a neuron spikes, its potential is reset to $0$ and all other neurons receive an additional amount $h/N$ of potential, where $ h >…
Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
We show that in a broad class of processes that show a $1/f^{\alpha}$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
A generic communication model of a boolean network with transmission errors is proposed to explore the power-law scaling of states' evolution in small-world networks. In the model, the power spectrum of the population difference between…
We study the work fluctuations of a particle, confined to a moving harmonic potential, under the influence of friction and external Poissonian shot noise. The asymmetry of the noise induces an effective nonlinearity in the potential, which…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied…
The scaling properties of oil price fluctuations are described as a non-stationary stochastic process realized by a time series of finite length. An original model is used to extract the scaling exponent of the fluctuation functions within…