Skip to search formSkip to main contentSkip to account menu
  • Publications
  • Influence
MULTIVARIATE NORMAL APPROXIMATION USING EXCHANGEABLE PAIRS
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of…
View PDF on arXiv
On Stein's method for multivariate normal approximation
The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-R\"ollin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The…
View PDF on arXiv
Limit theorems for Betti numbers of random simplicial complexes
There have been several recent articles studying homology of various types of random simplicial complexes. Several theorems have concerned thresholds for vanishing of homology, and in some cases…
View via Publisher
Exchangeable pairs and Poisson approximation
This is a survery paper on Poisson approximation using Stein's method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of…
View PDF on arXiv
The Random Matrix Theory of the Classical Compact Groups
View via Publisher
ON THE APPROXIMATE NORMALITY OF EIGENFUNCTIONS OF THE LAPLACIAN
The main result of this paper is a bound on the distance between the distribution of an eigenfunction of the Laplacian on a compact Riemannian manifold and the Gaussian distribution. If X is a random…
View PDF on arXiv
Spectral measures of powers of random matrices
This paper considers the empirical spectral measure of a power of a random matrix drawn uniformly from one of the compact classical matrix groups. We give sharp bounds on the $L_p$-Wasserstein…
View PDF on arXiv
Linear functions on the classical matrix groups
Let M be a random matrix in the orthogonal group On, distributed according to Haar measure, and let A be a fixed n x n matrix over R such that Tr(AA t ) = n. Then the total variation distance of the…
View PDF on arXiv
Projections of Probability Distributions: A Measure-Theoretic Dvoretzky Theorem
Many authors have studied the phenomenon of typically Gaussian marginals of high-dimensional random vectors; e.g., for a probability measure on \({\mathbb{R}}^{d}\), under mild conditions, most…
View PDF on arXiv
Approximation of Projections of Random Vectors
Let X be a d-dimensional random vector and Xθ its projection onto the span of a set of orthonormal vectors {θ1,…,θk}. Conditions on the distribution of X are given such that if θ is chosen according…
View on Springer
...
...
By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy, Terms of Service, and Dataset License