Notes from my course "Concentration of Measure on the Compact Classical Matrix Groups" at Women and Mathematics at the Institute for Advanced Study, 2014. These are rather rough and in particular are still lacking a lot of references and attributions. I am currently writing a monograph on the random matrix theory of the classical compact groups, which grew out of these notes. Comments/corrections/suggestions are welcome!
Video of my talk "Concentration of Spectral Measures of Random Matrices" at the IMA workshop Information Theory and Concentration Phenomena in April 2015.
Here are the slides from
"Uniformity of Eigenvalues of Some Random Matrices" at the 2014 Northeast Probability Seminar (held at Columbia University).
Here are the slides from a four-part mini-course "Randomness in geometry and topology: finding order in the chaos" at the 2013 – 2014 Low-dimensional Structure in High-dimensional Systems (LDHD) Summer School at SAMSI:
Linear Projections of High-Dimensional Data
Random Unitary Matrices and Friends
The Topology of Random Spaces
Stein's Method: The last gadget under the hood
Here are the slides from "The spectra
of powers of random unitary matrices" at the
Workshop on the Interplay of Banach Space Theory and Convex
Geometry and the Banff International Research Station. You can watch a video
of the talk!
Here are the slides from "Projections of Probability Distributions: A measure-theoretic Dvoretzky theorem" at the 2012 Midwest Probability Colloquium (held at Northwestern University).
When I was barely out of diapers, I was asked to give a talk on "How to prove a central limit theorem" at the Conference on Number Theory and Random Phenomena at the University of Bristol (March 2007). Here are scans of the slides. There's rather an overemphasis on Stein's method at the end (hey, I said I was barely out of diapers), but they're not bad as a quick and dirty introduction to some of the basic techniques.
The titles below are links to arXiv versions; the bibliographic entries are links to the published versions.
Personal Note: 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).
Please note: 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.