Related papers: Universal mesoscopic statistics and the localizati…
In the late seventies an increasing interest in the scaling theory of Anderson localization led to new efforts to understand the conductance of systems which scatter electrons elastically. The conductance and its relation to the scattering…
We analyze the propagation of gravitational waves in a medium containing bounded subsystems ("molecules"), able to induce significant Macroscopic Gravity effects. We establish a precise constitutive relation between the average quadrupole…
In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We study the intensity distribution function, P(I), for monochromatic waves propagating in quasi one-dimensional disordered medium, assuming that a point source and a point detector are embedded in the bulk of the medium. We find deviations…
The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the…
Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We use comparisons between the shapes of gravitational lens galaxies and models for their mass distributions to derive statistical constraints on the alignment of the mass distribution relative to the observed lens galaxy and on the…
We provide an introduction to complex photonic media, that is, composite materials with spatial inhomogeneities that are distributed over length scales comparable to or smaller than the wavelength of light. This blossoming field is firmly…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
An electromagnetic wave-packet propagating in a linear, homogeneous, and isotropic medium changes shape while its envelope travels with different velocities at different points in spacetime. In general, a wave-packet can be described as a…
We investigate statistical inference across time scales. We take as toy model the estimation of the intensity of a discretely observed compound Poisson process with symmetric Bernoulli jumps. We have data at different time scales:…
A study on the effects of optical gain nonuniformly distributed in one-dimensional random systems is presented. It is demonstrated numerically that even without gain saturation and mode competition, the spatial nonuniformity of gain can…
Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for…
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
A unified approach is proposed to describe the statistics of the short time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a…
Nonlinear disordered media uniquely combine multiple scattering and second-harmonic generation. Here, we investigate the statistical properties of the nonlinear light generated within such media. We report super-Rayleigh statistics of the…
A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…