Related papers: Some results on the optimal matching problem for t…
In this paper, we analyze the convergence rate of the Jacobi-Proximal Alternating Direction Method of Multipliers (ADMM) initially introduced by Deng et al. for the block-structured optimization problem with linear constraint. The algorithm…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in…
In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in…
In this paper, we study the probability density function, $\mathbb{P}(c,\alpha,\beta, n)\,dc$, of the center of mass of the finite $n$ Jacobi unitary ensembles with parameters $\alpha\,>-1$ and $\beta >-1$; that is the probability that…
We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…
Classical Jacobi polynomials $P_{n}^{(\alpha,\beta)}$, with $\alpha, \beta>-1$, have a number of well-known properties, in particular the location of their zeros in the open interval $(-1,1)$. This property is no longer valid for other…
Let $\mu$ be an Ahlfors-David probability measure on $\mathbb{R}^q$, namely, there exist some constants $s_0>0$ and $\epsilon_0,C_1,C_2>0$ such that \[ C_1\epsilon^{s_0}\leq\mu(B(x,\epsilon))\leq…
We investigate the average minimum cost of a bipartite matching between two samples of n independent random points uniformly distributed on a unit cube in d $\ge$ 3 dimensions, where the matching cost between two points is given by any…
In the hard edge scaling limit of the Jacobi unitary ensemble generated by the weight $x^{\alpha}(1-x)^{\beta},~x\in[0,1],~\alpha,\beta>0$, the probability that all eigenvalues of Hermitian matrices from this ensemble lie in the interval…
The paper studies the limiting behavior of spectral measures of random Jacobi matrices of Gaussian, Wishart and MANOVA beta ensembles. We show that the spectral measures converge weakly to a limit distribution which is the semicircle…
Let $\lambda$ and $\mu$ be beta-Jacobi and beta-Laguerre ensembles with joint density function $f_{\beta, m, a_1, a_2}$ and $f_{\beta, m, a_1}$, respectively. Here $\beta>0$ and $a_1, a_2$ and $m$ satisfying . $a_1,…
Let ${\bf P}_k^{(\alpha, \beta)} (x)$ be an orthonormal Jacobi polynomial of degree $k.$ We will establish the following inequality \begin{equation*} \max_{x \in [\delta_{-1},\delta_1]}\sqrt{(x- \delta_{-1})(\delta_1-x)}…
Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…
In dimension 2, we introduce a distributional Jacobian determinant $\det DV_\beta(Dv)$ for the nonlinear complex gradient $(x_1,x_2)\mapsto |Dv|^\beta(v_{x_1},-v_{x_2})$ for any $\beta>-1$, whenever $v\in W^{1,2 }_{\text{loc}}$ and $\beta…
Processing data collected by a network of agents often boils down to solving an optimization problem. The distributed nature of these problems calls for methods that are, themselves, distributed. While most collaborative learning problems…
This paper deals with studying vague convergence of random measures of the form $\mu_{n}=\sum_{i=1}^{n} p_{i,n} \delta_{\theta_i}$, where $(\theta_i)_{1\le i \le n}$ is a sequence of independent and identically distributed random variables…
In this paper, the moment problem for symmetric probability measures is characterized in terms of associated sequences called Jacobi sequences $\{\omega_n\}$. A notion named property (SC), which is proved to be a necessary and sufficient…
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…
We study the problem of aligning the supports of distributions. Compared to the existing work on distribution alignment, support alignment does not require the densities to be matched. We propose symmetric support difference as a divergence…