Related papers: Stein's method, heat kernel, and linear functions …
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…
A general method for the direct evaluation of the temperature dependence of the quantum-mechanical reaction rate constant in many-dimensional systems is described. The method is based on the quantum instanton approximation for the rate…
We develop Stein's method for the half-normal distribution and apply it to derive rates of convergence in distributional limit theorems for three statistics of the simple symmetric random walk: the maximum value, the number of returns to…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
We get a generalization of Krein's formula -which relates the resolvents of different selfadjoint extensions of a differential operator with regular coefficients- to the non-regular case $A=-\partial_x^2+(\nu^2-1/4)/x^2+V(x)$, where…
Stein's (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein's method, one needs to establish a Stein…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on…
Random features have been introduced to scale up kernel methods via randomization techniques. In particular, random Fourier features and orthogonal random features were used to approximate the popular Gaussian kernel. Random Fourier…
Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds…
For any integer $m<n$, where $m$ can depend on $n$, we study the rate of convergence of $\frac{1}{\sqrt{m}}\mathrm{Tr} \mathbf{U}^m$ to its limiting Gaussian as $n\to\infty$ for orthogonal, unitary and symplectic Haar distributed random…
As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low $10^{-18}$ range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
In this note we extend kernel function approximation results for neural networks with Gaussian-distributed weights to single-layer networks initialized using Haar-distributed random orthogonal matrices (with possible rescaling). This is…
The one parameter family of Jack(alpha) measures on partitions is an important discrete analog of Dyson's beta ensembles of random matrix theory. Except for special values of alpha=1/2,1,2 which have group theoretic interpretations, the…
This paper provides an introduction to the Stein method framework in the context of steady-state diffusion approximations. The framework consists of three components: the Poisson equation and gradient bounds, generator coupling, and moment…
For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the case that the only affordable operation is matrix-vector multiplication. In such case, randomized method is a powerful way to estimate the spectral density (or…
We consider the mean field analog of the p-star model for homogeneous random networks, and compare its behaviour with that of the p-star model and its classical mean field approximation in the thermodynamic regime. We show that the…
Thermodynamic properties of the quantum Heisenberg spin chains with S = 1/2, 1, and 3/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat,…