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MULTIVARIATE NORMAL APPROXIMATION USING EXCHANGEABLE PAIRS

- S. Chatterjee, Elizabeth S. Meckes
- Mathematics
- 16 January 2007

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… Expand

On Stein's method for multivariate normal approximation

- Elizabeth S. Meckes
- Mathematics
- 2 February 2009

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… Expand

Limit theorems for Betti numbers of random simplicial complexes

- Matthew Kahle, Elizabeth S. Meckes
- Mathematics
- 21 September 2010

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… Expand

Exchangeable pairs and Poisson approximation

- S. Chatterjee, P. Diaconis, Elizabeth S. Meckes
- Mathematics
- 23 November 2004

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… Expand

The Random Matrix Theory of the Classical Compact Groups

- Elizabeth S. Meckes
- Mathematics
- 5 September 2019

ON THE APPROXIMATE NORMALITY OF EIGENFUNCTIONS OF THE LAPLACIAN

- Elizabeth S. Meckes
- Mathematics
- 9 May 2007

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… Expand

Spectral measures of powers of random matrices

- Elizabeth S. Meckes, M. Meckes
- Mathematics
- 9 October 2012

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… Expand

Linear functions on the classical matrix groups

- Elizabeth S. Meckes
- Mathematics
- 20 September 2005

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… Expand

Projections of Probability Distributions: A Measure-Theoretic Dvoretzky Theorem

- Elizabeth S. Meckes
- Mathematics
- 16 February 2011

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… Expand

Approximation of Projections of Random Vectors

- Elizabeth S. Meckes
- Mathematics
- 10 December 2009

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… Expand

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