Related papers: Local Number Fluctuations in Hyperuniform and Nonh…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
The dependence of galaxy clustering on local density provides an effective method for extracting non-Gaussian information from galaxy surveys. The two-point correlation function (2PCF) provides a complete statistical description of a…
We study second-order cosmological perturbations in scalar-tensor models of dark energy that satisfy local gravity constraints, including f(R) gravity. We derive equations for matter fluctuations under a sub-horizon approximation and…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
We analyze particle number fluctuations in the crossover region near the critical endpoint of a first-order phase transition by utilizing molecular dynamics simulations of the classical Lennard-Jones fluid. We extend our previous study…
A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is…
Cluster abundance measurements are among the most sensitive probes of the amplitude of matter fluctuations in the universe, which in turn can help constrain other cosmological parameters, like the dark energy equation of state or neutrino…
We discuss fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies for extracting information concerning such local order from…
We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…
We derive fundamental accuracy limits for distributed localization when a fusion center has access only to independently rate-distortion (RD)-optimally compressed versions of multi-sensor observations, under a line-of-sight propagation…
Probability distributions defined on the unit interval are widely used in fields ranging from econometrics to reliability studies. Traditional models such as the beta and Kumaraswamy distributions are well-established due to their…
We focus on the localized phase of pinning models with i.i.d. site disorder on which we assume only that the moment generating function is bounded in a neighborhood of the origin. We develop quantitative correlation functions estimates for…
The increasing precision in the determination of the Hubble parameter has reached a per cent level at which large-scale cosmic flows induced by inhomogeneities of the matter distribution become non-negligible. Here we use large-scale…
High-dimensional sample correlation matrices are a crucial class of random matrices in multivariate statistical analysis. The central limit theorem (CLT) provides a theoretical foundation for statistical inference. In this paper, assuming…
We show that quasi-long-range (QLR) pair correlations that decay asymptotically with scaling $r^{-(d+1)}$ in $d$-dimensional Euclidean space $\mathbb{R}^d$, trademarks of certain quantum systems and cosmological structures, are a universal…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
In this paper, we use the framework of mod-$\phi$ convergence to prove precise large or moderate deviations for quite general sequences of real valued random variables $(X_{n})_{n \in \mathbb{N}}$, which can be lattice or non-lattice…
The non-Gaussian distribution of primordial perturbations has the potential to reveal the physical processes at work in the very early Universe. Local models provide a well-defined class of non-Gaussian distributions that arise naturally…
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…