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content/Math401/Math401_P1_2.md

@@ -66,7 +66,9 @@ The Haar measure is the unique probability measure that is invariant under the a
 
 _The existence and uniqueness of the Haar measure is a theorem in compact lie group theory. For this research topic, we will not prove it._
 
-### Sub-Gaussian concentration
+### Maxwell-Boltzmann distribution and projection of high-dimensional sphere
+
+
 
 ### Random sampling on the $CP^n$
 
@@ -90,9 +92,6 @@ $$
 S_{m,n}=\sum_{k=n+1}^{mn}\frac{1}{k}-\frac{m-1}{2n}\simeq \ln m-\frac{m}{2n}
 $$
 
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 ## References
 
 - [The random Matrix Theory of the Classical Compact groups](https://case.edu/artsci/math/esmeckes/Haar_book.pdf)