Stein's Method Papers
Some papers which have more complicated examples
Concentration Inequalities/Concentration of Measure
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.
Dirichlet Processes and Lévy Processes
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