# A simplified proof of CLT for convex bodies

## TL;DR

This paper offers a concise, accessible proof of Klartag's central limit theorem for convex bodies, relying solely on classical properties of log-concave functions, and includes an appendix linking thin shell conditions to CLT.

## Contribution

The paper provides a simplified, elementary proof of the CLT for convex bodies, making the result more accessible and connecting thin shell properties to the CLT.

## Key findings

- Simplified proof of Klartag's CLT for convex bodies
- Demonstrates that thin shell condition implies CLT
- Accessible approach using classical log-concave function facts

## Abstract

We present a short proof of Klartag's central limit theorem for convex bodies, using only the most classical facts about log-concave functions. An appendix is included where we give the proof that thin shell implies CLT. The paper is accessible to anyone.