# Topics

## Stein's Method Papers

- A good first paper to look at. At least least the start. There are many (too many ?) examples: Reinert Stein
- Another good intro paper. A bit more "Mathematized": Persi Diaconis
- Some details of the computation from February 10: Stein notes
- Chatterjee's lecture note on Stein's method: http://www.stat.berkeley.edu/~sourav/stat206Afall07.html

### Some papers which have more complicated examples

- Using Stein's Method with Malliavin Calculus: Maliiavin Calc
- Application to Multivariate Gaussians: Multivariate Gaussian
- Stein's method for concentration inequalities
- Stein's method for Spectral Graph Theory http://arxiv.org/abs/math.PR/0605552

## Concentration Inequalities/Concentration of Measure

- R. Vershynin's lecture notes, including a summary of useful concentration inequalities and applications (Lectures 1-4).
- G. Lugosi's lecture notes
- A. Barvinok's lecture notes

- M. Ledoux's webpage contains several relevant publications of interest.

## Random Matrices Papers

- R. Vershynin's lecture notes, covering bounds on largest and smallest singular values of Gaussian random matrices and generalizations thereof.
- I. Johnstone's paper On the distribution of the largest eigenvalue in principal components analysis
- Recent papers by R. Vershynin, in particular on the smallest singular value of a random matrix, and on product of a deterministic and a random matrix
- An elementary proof of the Johnson-Lindenstrauss lemma by Sanjoy Dasgupta, Anupam Gupta. This describes one the most basic applications of random matrices (more precisely, random projections) to metric embeddings. An overview of related techniques, especially in the graph setting, is provided by The geometry of graphs and some of its algorithmic applications by Nathan Linial, Eran London, Yuri Rabinovich. Some of the state-of-art metric embedding results can be found in Measured descent: A new embedding method for finite metrics (and references therein) by Robert Krauthgamer, James R. Lee, Manor Mendel, Assaf Naor. One of the oldies that inspired much of this is On lipschitz embedding of finite metric spaces in Hilbert space by Jean Bourgain.
- Local operator theory, random matrices and Banach spaces by S. Szarek and K.R. Davidson, on connections between random matrices, local theory of Banach spaces, asymptotic and non-asymptotic results in random matrix theory.

## Compressed Sensing

- A page containing lots of references to articles, tutorials, code etc... is the Compressive Sensing Resources page a Rice.
- The Dantzig Selector: Statistical estimation when p is much larger than n, Emmanuel Candès and Terence Tao.
- The recent Duke Compressed Sensing workshop also has all the talks and videos of the talks online.

## Dirichlet Processes and Lévy Processes

- A constructive definition of Dirichley priors by J. Sethuraman.
- Robert's talks (1 and 2)/handouts have been uploaded in the attachments session.

## Random walks

- Diaconis--Graham, Asymptotic analysis of a random walk on a hypercube with many dimensions
- Aldous--Diaconis, Shuffling Cards and Stopping Times

## The Berry-Esseen Theorem and Edgeworth Expansion

- Balachandran, Prakash. The Edgeworth Expansion and Convergence in the Central Limit Theorem
- Bhattacharya, R.N., Rao, R. Normal Approximations and Asymptotic Expansions.
- Billingsley, Patrick. Probability and Measure.
- Chung, Kai Lai. A Course in Probability Theory.
- Feller, William. An Introduction to Probability Theory and its Applications, Volumes I and II.
- Hall, Peter. The Bootstrap and Edgeworth Expansion.

## Weak Numerical Methods

Mariko Ninomiya and Syoiti Ninomiya - 2009 - A new higher-order weak approximation scheme for s.pdf

Kusuoka - 2004 - Approximation of expectation of diffusion processe.pdf

Ninomiya and Victoir - 2008 - Weak approximation of stochastic differential equa.pdf