Related papers: Multifractal analysis with the probability density…
The nature of the critical point of the Anderson transition in high magnetic fields is discussed with an emphasis on scale invariance and universality of the critical exponent. Special attention is paid to the distribution function of the…
This letter provides the first prediction of the probability density function (PDF) of flux $R$ in plasma sheath sheath region in magnetic fusion devices which is characterized by dynamical equations with exponential non-linearities. By…
Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with…
The gravitational evolution of the cosmic one-point Probability Distribution Function (PDF) can be estimated using an analytic approximation that combines gravitational Perturbation Theory (PT) with the Edgeworth expansion around a Gaussian…
A robust uncertainty estimate in global analyses of Parton Distribution Functions (PDFs) is essential at the Large Hadron Collider (LHC), especially in view of the high-precision data anticipated by experimentalists in the High-Luminosity…
The one-point probability distribution function (PDF) is a powerful summary statistic for non-Gaussian cosmological fields, such as the weak lensing (WL) convergence reconstructed from galaxy shapes or cosmic microwave background (CMB)…
The analysis of the Lyman-alpha forest of absorption lines in quasar spectra has emerged as a potentially powerful technique to constrain the linear matter power spectrum. In most previous work, the amplitude of the ionizing background was…
Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using…
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…
We study the nature of the phase transition in the multifractal formalism of the harmonic measure of Diffusion Limited Aggregates (DLA). Contrary to previous work that relied on random walk simulations or ad-hoc models to estimate the low…
At Anderson critical points, the statistics of the two-point transmission $T_L$ for disordered samples of linear size $L$ is expected to be multifractal with the following properties [Janssen {\it et al} PRB 59, 15836 (1999)] : (i) the…
We explore the multifractality of the steady state wave function in non-unitary random quantum dynamics in one dimension. We focus on two classes of random systems: the hybrid Clifford circuit model and the non-unitary free fermion…
We introduce the Fluctuating Two-Ray (FTR) fading model, a new statistical channel model that consists of two fluctuating specular components with random phases plus a diffuse component. The FTR model arises as the natural generalization of…
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of…
Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…
In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent $\tau(q)$ is related…
We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation…
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large…
We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…