相关论文: On the expected L2-discrepancy of jittered samplin…
Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such…
We prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous…
The leptonic QED radiative corrections are calculated in the next-to-leading log approximation ${\cal O}[\alpha^2 \ln(Q^2/m_e^2)]$ for unpolarized deeply inelastic $ep$--scattering in the case of mixed variables. The corrections are…
We consider the 2-dimensional random matching problem in $\mathbb{R}^2.$ In a challenging paper, Caracciolo et. al. arXiv:1402.6993 on the basis of a subtle linearization of the Monge Ampere equation, conjectured that the expected value of…
Let K be a d-dimensional convex body, and let $K^{(n)}$ be the intersection of n halfspaces containing $K$ whose bounding hyperplanes are independent and identically distributed. Under suitable distributional assumptions, we prove an…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
A new approach on the joint estimation of partially exchangeable observations is presented by constructing pairwise dependence between $m$ random density functions, each of which is modeled as a mixture of geometric stick breaking…
Recent analysis of the divergence constraint in the incompressible Stokes/Navier--Stokes problem has stressed the importance of equivalence classes of forces and how it plays a fundamental role for an accurate space discretization. Two…
Mixtures of multivariate contaminated shifted asymmetric Laplace distributions are developed for handling asymmetric clusters in the presence of outliers (also referred to as bad points herein). In addition to the parameters of the related…
The {\em Maximal} points in a set S are those that aren't {\em dominated} by any other point in S. Such points arise in multiple application settings in which they are called by a variety of different names, e.g., maxima, Pareto optimums,…
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of…
This paper addresses the problem of estimating the containment and similarity between two sets using only random samples from each set, without relying on sketches of full sets. The study introduces a binomial model for predicting the…
We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…
In this note we show that the volume of axis-parallel boxes in $\mathbb{R}^d$ which do not intersect an admissible lattice $\mathbb{L}\subset\mathbb{R}^d$ is uniformly bounded. In particular, this implies that the dispersion of the dilated…
To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\"{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and…
We consider the fluctuations in the number of particles in a box of size L^d in Z^d, d>=1, in the (infinite volume) translation invariant stationary states of the facilitated exclusion process, also called the conserved lattice gas model.…
The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square $[0,1]^2$ to approach a stationary distribution with density proportional to…
Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $\theta \in…
We present a systematic study of the nested sampling algorithm based on the example of the Potts model. This model, which exhibits a first order phase transition for $q>4$, exemplifies a generic numerical challenge in statistical physics:…
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In…