---
tags: concentration
---
Overview and References
===
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## References
---
### Concentration Inequalities
- [A brief note on Concentration Inequalities](http://www.econ.upf.edu/~lugosi/mlss_conc.pdf)
- by the authors of the text we are using... I plan to cover all of the results in this note (with proofs) by semester end

- [Terrence Tao's Notes on Concentration Inequalities](https://terrytao.wordpress.com/2010/01/03/254a-notes-1-concentration-of-measure/)
- As Michael Steele says, "Terrence Tao is on everyone's list of top living mathematicians"

- [Concentration Inequalities - Steve Lalley](https://galton.uchicago.edu/~lalley/Courses/386/Concentration.pdf)
- Notes by the most exciting professor I had in my student life (these notes have a few constants off)

- [Note on Paley-Zygmund Argument \& three Variations](
http://www-stat.wharton.upenn.edu/~steele/Courses/530/Resources/Lower%20Bounds/LowerBounds.pdf)
- Michael Steele is a brilliant probabilist who writes amazing well. The essence of this note is that for lower bound on probabilities think Cauchy-Schwartz. Who else would write this but the author of the [C-S Master Class](https://www.maa.org/press/maa-reviews/the-cauchy-schwarz-master-class-an-introduction-to-the-art-of-mathematical-inequalities)! Thanks to Sam for sharing this!!

- [Martin Wainwright's Chapter on Tail Bounds](https://www.stat.berkeley.edu/~mjwain/stat210b/Chap2_TailBounds_Jan22_2015.pdf)
- This chapter is from a upcoming book by the author titled *High-dimensional statistics: A non-asymptotic viewpoint* that will be published in 01/2019. I like the exercises, and his development is in some places complementary to the lectures by the probabilists.

- Some More Notes on Concentration Inequalities

- [Lugosi](http://www.econ.upf.edu/~lugosi/anu.pdf)

- [McDiarmid](http://cgm.cs.mcgill.ca/~breed/conc/colin.pdf)

### Background
---
- [My favorite Measure Theoretic Probability Theory Book](https://services.math.duke.edu/~rtd/PTE/PTEv5a.pdf)
- Good things in life are often available for no cost

- [Note on Fourier Analysis on the Cube](https://theoryofcomputing.org/articles/gs001/gs001.pdf)
- I referred to this for construction of a *large number* of pairwise independent symmetric Bernoulli's.