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content/Math401/Math401_P1_3.md

@@ -1,8 +1,9 @@
 # Math 401, Paper 1, Side note 3: Levy's concentration theorem
 
-## Levy's concentration theorem in _High-dimensional probability_ by Roman Vershynin
+## Basic definitions
+
+### Lipschitz function
 
-### Levy's concentration theorem (Vershynin's version)
 
 #### $\eta$-Lipschitz function
 
@@ -16,6 +17,16 @@ for all $x,y\in X$. And $\eta=\|f\|_{\operatorname{Lip}}=\inf_{L\in \mathbb{R}}L
 
 That basically means that the function $f$ should not change the distance between any two pairs of points in $X$ by more than a factor of $L$.
 
+### Sub-Gaussian concentration
+
+### Random sampling on the $CP^n$
+
+
+
+## Levy's concentration theorem in _High-dimensional probability_ by Roman Vershynin
+
+### Levy's concentration theorem (Vershynin's version)
+
 > This theorem is exactly the 5.1.4 on the _High-dimensional probability_ by Roman Vershynin.
 
 #### Isoperimetric inequality on $\mathbb{R}^n$