Related papers: Estimating Support Functions of Random Polytopes v…
We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and…
Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal…
Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…
We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…
Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan…
Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of…
In this paper we give a formula for the probability that $n$ random points chosen under the uniform distribution in a disk are in convex position. While close, the formula is recursive and is totally explicit only for the first values of…
We consider \emph{random linear programs} (rlps) as a subclass of \emph{random optimization problems} (rops) and study their typical behavior. Our particular focus is on appropriate linear objectives which connect the rlps to the mean…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
For frequentist settings in which parameter randomness represents variability rather than uncertainty, the ideal measure of the support for one hypothesis over another is the difference in the posterior and prior log odds. For situations in…
We use the notions of reflexivity and of reflexive dimensions in order to introduce probability measures for lattice polytopes and initiate the investigation of their statistical properties. Examples of applications to discrete geometry…
In this paper,we consider the solutions of the non-homogeneous elliptic obstacle problems with Orlicz growth involving measure data. We first establish the pointwise estimates of the approximable solutions to these problems via fractional…
We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear…
We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
We study the uniform asymptotics for the orthogonal polynomials with respect to weights composed of both absolutely continuous measure and discrete measure, by taking a special class of the sieved Pollazek Polynomials as an example. The…
The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…
The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…