Elizabeth Meckes's research

Monograph

The Random Matrix Theory of the Classical Compact Groups

Cambridge University Press, 2019.

Full text (pre-copy editing version; page numbers may differ from the final version)

Review by Ofer Zeitouni for the Bulletin of the American Mathematical Society.

Research papers

Fluctuations of the spectrum in rotationally invariant random matrix ensembles (with Mark Meckes) — to appear in Random Matrices Theory Appl.
Eigenvalue rigidity for truncations of random unitary matrices (with Kathryn Stewart) — to appear in Random Matrices Theory Appl.
On the eigenvalues of truncations of random unitary matrices (with Kathryn Stewart) — Electron. Comm. Probab., Vol. 24(57), 2019.
Random matrices with prescribed eigenvalues and expectation values for random quantum states (with Mark Meckes) — Trans. Amer. Math Soc. 373, 2020.
Convergence rates of the empirical spectral measure of unitary Brownian motion (with Tai Melcher) — Annales Henri Lebesgue, Vol. 1 (2018).
A sharp rate of convergence for the empirical spectral measure of a random unitary matrix (with Mark Meckes) — Zapiski Seminarov POMI 457 (V. N. Sudakov memorial volume) (also to be reprinted in Journal of Mathematical Sciences).
Rates of convergence for empirical spectral measures: a soft approach (with Mark Meckes) — in Convexity and Concentration (The IMA Volumes in Mathematics and its Applications), Springer (2017).
Almost sure convergence in quantum spin glasses (with David Buzinski) — J. Math. Phys. 56, 123304 (2015).
Self-similarity in the circular unitary ensemble (with Mark Meckes) — Discrete Analysis (2016).
A rate of convergence for the circular law for the complex Ginibre ensemble (with Mark Meckes) — Annales de la Faculté des Sciences de Toulouse (6) 24, no. 1 (2015).
On the equivalence of modes of convergence for log-concave measures (with Mark Meckes) — Geometric Aspects of Functional Analysis: Papers from the Israel Seminar (GAFA). (Springer Lecture Notes Vol. 2116, 2014).
Spectral measures of powers of random matrices (with Mark Meckes) — Electron. Comm. Probab. 18, no. 78 (2013).
Dedicated to the memory of Helen Murphy Tepperman.
Asymptotics of the mean-field Heisenberg model (with Kay Kirkpatrick) — J. Stat. Phys 152, no. 1 (2013).
Concentration and convergence rates for spectral measures of random matrices (with Mark Meckes) — Probab. Theory Related Fields 156, no. 1-2 (2013).
Elizabeth's personal note on this paper: I think of this paper as being unofficially dedicated to our children: Peter, who stubbornly refused to be born while most of the work in this paper was done; and Juliette, who told me one morning that it would make her happy if I proved a theorem that day (I'm pretty sure it was what became Theorem 3.5).
Projections of probability distributions: A measure-theoretic Dvoretzky theorem — in Geometric Aspects of Functional Analysis: Papers from the Israel Seminar (GAFA) , (Springer Lecture Notes Vol. 2050, 2012).
Limit theorems for Betti numbers of random simplicial complexes (with Matthew Kahle) — Homology, Homotopy and Applications 15, no. 1 (2013). Erratum
Another observation about operator compressions (with Mark Meckes) — Proc. Amer. Math. Soc. 139 (2011).
Approximation of projections of random vectors — J. Theoret. Probab. 25, no. 2 (2012).
Correction: In the published version of this paper, there is a misprint in the last sentence of the abstract; it says there that k=c(log(d)); it should have been k=c(√log(d)). For the sharp rate, see the paper "Projections of probability distributions: A measure-theoretic Dvoretzky theorem" above.
On Stein's method for multivariate normal approximation — in High Dimensional Probability V: The Luminy Volume (IMS Collections Vol. 5, 2009).
Quantitative asymptotics of graphical projection pursuit — Electron. Comm. Probab. 14 (2009).
On the approximate normality of eigenfunctions of the Laplacian — Trans. Amer. Math. Soc. 361, no. 10 (2009).
Multivariate normal approximation using exchangeable pairs (with Sourav Chatterjee) — ALEA 4 (2008).
Linear functions on the classical matrix groups — Trans. Amer. Math. Soc. 360, no. 10 (2008).
The central limit problem for random vectors with symmetries (with Mark Meckes) — J. Theoret. Probab. 20, no. 4 (2007).
Exchangeable pairs and Poisson approximation (with Sourav Chatterjee and Persi Diaconis) — Probab. Surv. 2 (2005).

PhD thesis

An Infinitesimal Version of Stein's Method of Exchangeable Pairs, Stanford University, 2006.

Other papers written under Elizabeth's mentorship

David Judkovich, The cycle structure of permutations without long cycles.
Kathryn Stewart, Total variation approximation of random orthogonal matrices by Gaussian matrices, J. Theoret. Probab. 33 (2020).
Sang Du and Mark Syvuk, Comparison of f-vectors of random polytopes to the Gaussian distribution.

Erdős number

2