---
# System prepended metadata

title: '18.656 Lecture 3 Reading Notes: Sub-exponential variables, Azuma-Hoeffding and applications'
tags: [Eva]

---

# 18.656 Lecture 3 Reading Notes: Sub-exponential variables, Azuma-Hoeffding and applications

###### tags: `Eva`
```
-- Chapter 2.1 on sub-exponential variables.   
We will explore some algorithmic consequences 
for randomized dimensionality reduction 
(see Example 2.12 on Johnson-Lindenstrauss).

-- Chapter 2.2 on Azuma-Hoeffiding and martingale methods:  
we will cover this material just briefly.  
It is worth reading in more depth to gain 
a more complete understanding of a broader arsenal of tools.
```

## 1. Sub-exponential variables *(Chapter 2.1.3)*
As a relaxation of sub-guassianity, sub-exponential variables are defined by a slightly milder condition on the MGF.


![](https://i.imgur.com/s6ukvmY.png)

Any sub-Gaussian variable is also sub-exponential ($v = \sigma, \alpha = 0$), but the converse is not true.



## 2. Azuma-Hoeffding and applications