Related papers: Probability distributions with singularities
We obtain some theoretic and experimental results concerning various properties (the number of fixed points, image distribution, cycle lengths) of the dynamical system naturally associated with Fermat quotients acting on the set $\{0, ...,…
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…
This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…
Time evolution equation for the Probability Distribution Function (PDF) is derived for system of weakly interacting waves. It is shown that a steady state for such system may correspond to strong intermittency.
A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary…
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
Active contributions to fluctuations are a direct consequence of metabolic energy consumption in living cells. Such metabolic processes continuously create active forces, which deform the membrane to control motility, proliferation as well…
Detailed fluctuation theorems are statements about the probability distribution for the stochastic entropy production along a trajectory. It involves the consideration of a suitably transformed dynamics, such as the time reversed, the…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
Inhomogeneous environments are rather ubiquitous in nature, often implying anomalies resulting in deviation from Gaussianity of diffusion processes. While sub- and superdiffusion are usually due to conversing environmental features…
Non-equilibrium stationary fluctuations may exhibit a special symmetry called fluctuation relations (FR). Here, we show that this property is always satisfied by the subtraction of two random and independent variables related by a…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
Although regular conditional distributions (r.c.d.) are well-defined and widely used measure-theoretic objects, they can violate our intuition from the classical definition of a conditional probability given an event. For that purpose, the…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
We analyze the probabilities of large infrequent fluctuations in systems driven by external fields. In a broad range of the field magnitudes, the logarithm of the fluctuation probability is linear in the field magnitude, and the response…
The phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically. The possibility of social behaviors affecting the migration strategies has been taken into…
We will discuss the link between scientific explanations and probabilities, specially in relationship with statistical mechanics and the derivation of macroscopic laws from microscopic ones.
Traditionally, it is understood that fluctuations in the equilibrium distribution are not evident in thermodynamic systems of large $N$ (the number of particles in the system) \cite{Huang1}. In this paper we examine the validity of this…
We provide a scenario for a singularity-mediated turbulence based on the self-focusing non-linear Schr\"odinger equation, for which sufficiently smooth initial states leads to blow-up in finite time. Here, by adding dissipation, these…