相关论文: On Low-Dimensional Projections of High-Dimensional…

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…

The long-standing question of finding the momentum representation for the s-wave zero-range interaction in three spatial dimensions is here solved. This is done by expressing a certain distribution, introduced in a formal way by S. Tan…

Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…

Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…

We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…

Random effects meta-analysis is a widely applied methodology to synthetize research findings of studies in a specific scientific question. Besides estimating the mean effect, an important aim of the meta-analysis is to summarize the…

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

We describe the approach to lattice extraction of Generalized Parton Distributions (GPDs) that is based on the use of the double distributions (DDs) formalism within the pseudo-distribution framework. The advantage of using DDs is that GPDs…

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological…

Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…

Using our formalism of parton virtuality distribution functions (VDFs) we establish a connection between the transverse momentum dependent distributions (TMDs) ${\cal F} (x, k_\perp^2)$ and quasi-distributions $Q(y,P_z)$ introduced recently…

It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point…

A coordinate system is constructed for a general accelerating observer in 1+1 dimensions, and is used to determine the particle density of the massless Dirac vacuum for that observer. Equations are obtained for the spatial distribution and…

The spectral properties of the Laplacian operator on ``small-world'' lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a…

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…

Although time-dependent random media with short range correlations lead to (possibly biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable direction. This was pointed out recently in 1D lattice random…

We introduce a general expression which enables the parton distribution, unintegrated over the parton transverse momentum, to be obtained from the conventional parton densities. We use the formalism to study the effects of the transverse…

The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…

Random walks of n steps taken into independent uniformly random directions in a d-dimensional Euclidean space (d larger than 1), are named Dirichlet when their step lengths are distributed according to a Dirichlet law. The latter continuous…

Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…