Related papers: Statistics of the Mesoscopic Field
Using the path integral approach, we obtain the characteristic functions of the gyration radius distributions for Gaussian star and Gaussian rosette macromolecules. We derive the analytical expressions for cumulants of the both…
We report time-resolved measurements of the statistics of pulsed transmission through quasi-one-dimensional dielectric media with static disorder. The normalized intensity correlation function with displacement and polarization rotation for…
A single permutation, seen as union of disjoint cycles, represents a regular graph of degree two. Consider $d$ many independent random permutations and superimpose their graph structures. It is a common model of a random regular (multi-)…
We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and…
We follow the temporal evolution of mesoscopic intensity fluctuations and correlation in strongly localized samples. We find an initial burst in relative transmission fluctuations in random one dimensional (1D) samples due to fluctuations…
Threshold biasing of a Gaussian random field gives a linear amplification of the reduced two point correlation function at large distances. We show that for standard cosmological models this does not translate into a linear amplification of…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of the method of distribution functions in coordinate-momentum space that provides a detailed description of photon systems. We find that…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
The ionized interstellar medium disperses pulsar radio signals, resulting in a stochastic time-variable delay known as the dispersion measure (DM) noise. In the wideband paradigm of pulsar timing, we measure a DM together with a time of…
Precise characterization of the mutual information of MIMO systems is required to assess the throughput of wireless communication channels in the presence of Rician fading and spatial correlation. Here, we present an asymptotic approach…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
The distribution of the polarization of the Cosmic Microwave Background (CMB) in the sky is determined by the hypothesis of random Gaussian distribution of the primordial density perturbations. This hypotheses is well motivated by the…
Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
A random Gaussian density field contains a fixed amount of Fisher information on the amplitude of its power spectrum. For a given smoothing scale, however, that information is not evenly distributed throughout the smoothed field. We…