Proofs of Central limit theorem
- Method of characteristics
http://www.cs.toronto.edu/~yuvalf/CLT.pdf
- Method of Moments
http://www.cs.toronto.edu/~yuvalf/CLT.pdf
- Minimizing Entropy
“An information-theoretic proof of the central limit theorem with the Lindeberg condition” - Heat equation
Kolmogorov Petrovsky - Stein’s method
https://normaldeviate.wordpress.com/2013/11/16/steins-method/