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

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The…

We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…

The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue…

A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…

Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…

Statistical inference about the average effect in random-effects meta-analysis has been considered insufficient in the presence of substantial between-study heterogeneity. Predictive distributions are well-suited for quantifying…

We study the scattering dynamics of an $n$-component spinor wavefunction in a random environment on a two-dimensional lattice. In the presence of particle-hole symmetry we find diffusion on large scales. The latter is described by a…

The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…

We consider the modulation of data given by random vectors $X_n \in \mathbb{R}^{d_n}$, $n \in \mathbb{N}$. For each $X_n$, one chooses an independent modulating random vector $\Xi_n \in \mathbb{R}^{d_n}$ and forms the projection $Y_n =…

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…

Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron.…

Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…

We study properties of compactly supported, 4 parameter \newline $(\rho _{12},\rho _{23},\rho _{13},q)\in (-1,1)^{\times 4}$ family of continuous type 3 dimensional distributions, that have the property that for $q\rightarrow 1^{-}$ this…

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…

We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions in curved (or droplet) geometry. We show that for short time $t$, the probability distribution $P(H,t)$ of the height $H$ at a given point $x$…

Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…

Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and…

This note attempts to revisit the classical results on Laplace approximation in a modern non-asymptotic and dimension free form. Such an extension is motivated by applications to high dimensional statistical and optimization problems. The…

We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression…

An $(n,k)$-Poisson Multinomial Distribution (PMD) is the distribution of the sum of $n$ independent random vectors supported on the set ${\cal B}_k=\{e_1,\ldots,e_k\}$ of standard basis vectors in $\mathbb{R}^k$. We prove a structural…