相关论文: Large Deviations for Statistics of Jacobi Process

We define and study a multidimensional process that generalizes the eigenvalues of matrix Jacobi processes on the one hand and whose stationary distribution is given by the beta Jacobi ensemble on the other hand.

We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…

Some weighted inequalities for the maximal operator with respect to the discrete diffusion semigroups associated with exceptional Jacobi and Dunkl-Jacobi polynomials are given. This setup allows to extend the corresponding results obtained…

The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with…

This paper presents a novel Jacobi-style iteration algorithm for solving the problem of distributed submodular maximization, in which each agent determines its own strategy from a finite set so that the global submodular objective function…

Coefficients of super Jacobi polynomials of type $B(1,n)$ are rational functions in three parameters $k,p,q$. At the point $(-1,0,0)$ these coefficient may have poles. Let us set $q=0$ and consider pair $(k,p)$ as a point of $\Bbb A^2$. If…

We introduce a probabilistic representation of the derivative of the semigroup associated to a multidimensional killed diffusion process defined on the half-space. The semigroup derivative is expressed as a functional of a process that is…

We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial…

We present a holomorphic representation of the Jacobi algebra $\mathfrak{h}_n\rtimes \mathfrak{sp}(n,\R)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}^n\times \mathcal{D}_n$. We construct…

We develop direct and inverse scattering theory for Jacobi operators with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give a complete characterization of…

Let us consider a cyclic extension of a function field defined over a finite field. For a character (non-trivial) of this extension, we calculate, as a linear combinations of products of Jacobi sums, the coefficients of the polynomial given…

Let $\Delta$ be the Jacobi Laplacian. We study the chaotic and hypercyclic behaviour of the strongly continuous semigroups of operators generated by perturbations of $\Delta$ with a multiple of the identity on $L^p$ spaces.

The theory of spectral methods for partial differential equations leads to infinite-dimensional matrices which represent the derivative operator with respect to an underlying orthonormal basis. Favourable properties of such differentiation…

We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence…

This paper presents a Jacobi-type iteration for computing a given specified eigenpair of a symmetric matrix. For a certain class of diagonally dominant matrices, the procedure is shown to converge at a linear rate depending on how the…

We prove the large deviation principle for the supports of Jacobi ensembles following Guionnet's method.

Infinitesimal holomorphic realizations for the Schr\"{o}dinger-Weil representation and the discrete series representations of the Jacobi group are constructed. Explicit expressions of the basic differential operators are obtained. The…

There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to the same…

In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a…