Related papers: A characterization of the Riesz distribution
We continue our analysis of bad theories, focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers…
This paper proposes the density and characteristic functions of a general matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} = \mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution and…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…
We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz-Dunford functional calculus. Compared to related schemes, the new…
We develop a general method to quantify the uncertainties of parton distribution functions and their physical predictions, with emphasis on incorporating all relevant experimental constraints. The method uses the Hessian formalism to study…
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…
The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of…
We introduce a partition of (coweight) lattice points inside the dilated fundamental parallelepiped into those of partially closed simplices. This partition can be considered as a generalization and a lattice points interpretation of the…
A tempered version of the discrete Linnik distribution is introduced in order to obtain integer-valued distribution families connected to stable laws. The proposal constitutes a generalization of the well-known Poisson-Tweedie law, which is…
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this…
Suppose we are given two datasets: a labeled dataset and unlabeled dataset which also has additional auxiliary features not present in the first dataset. What is the most principled way to use these datasets together to construct a…
Some remarkable properties of the beta distribution are based on relations involving independence between beta random variables such that a parameter of one among them is the sum of the parameters of an other (see (1.1) et (1.2) below).…
Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…
We a present and analyze rpCholesky-QR, a randomized preconditioned Cholesky-QR algorithm for computing the thin QR factorization of real mxn matrices with rank n. rpCholesky-QR has a low orthogonalization error, a residual on the order of…
Zariski dense collections of quadratic points on curves $X$ are well-understood by results of Harris--Silverman and Vojta, but when $\dim X \geq 2$ there is not an analogous geometric characterization, even conjecturally. In this note we…
This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately…
We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…