相关论文: Stein kernels and moment maps

In this paper, we propose a free analogue to Fathi's construction of Stein kernels using moment maps (2019). This is possible for a class of measures called free moment measures that was introduced in the free case by Bahr and Boschert…

We establish existence of Stein kernels for probability measures on $\mathbb{R}^d$ satisfying a Poincar\'e inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are…

Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…

We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…

Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation and can be computed even when the target density has an intractable normalizing constant. Notable applications include the diagnosis of approximate MCMC…

We derive explicit central moment inequalities for random variables that admit a Stein coupling, such as exchangeable pairs, size--bias couplings or local dependence, among others. The bounds are in terms of moments (not necessarily…

We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate…

We consider a class of maps from integral Hankel operators to Hankel matrices, which we call restriction maps. In the simplest case, such a map is simply a restriction of the integral kernel onto integers. More generally, it is given by an…

In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established:…

We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central…

We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge-Amp\`{e}re equation. We prove an ABP estimate and a Harnack inequality and derive H\"{o}lder and…

In this work, we describe new constructions of free Stein kernels. Firstly, in dimension one, we propose a free analog to the construction of Stein kernels using moment maps as the one proposed by Fathi. This will be possible for a class of…

The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of…

In this paper, we study the modulus of continuity of solutions to Dirichlet problems for complex Monge-Amp\`ere equations with $L^p$ densities on Stein spaces with isolated singularities. In particular, we prove such solutions are H\"older…

We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…

We define a new type of wavelet frame adapted to the study of wave equations, that we call Minkowski curvelets, by reference to the curvelets introduced by Cand\`es, Demanet and Donoho. These space-time, strongly anisotropic, directional…

We study the parameter dependence of complex geodesics with prescribed boundary value and direction on bounded strongly linearly convex domains. As an important application we establish a quantitative relationship between the regularity of…

We investigate links between the so-called Stein's density approach in dimension one and some functional and concentration inequalities. We show that measures having a finite first moment and a density with connected support satisfy a…

In this paper we correct a gap of Whyburn type topological lemma and establish two superior limit theorems. As the applications of our Whyburn type topological theorems, we study the following Monge-Amp\`{e}re equation \begin{eqnarray}…

Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is given by an explicit formula, and the other via free…