# Random polytopes: central limit theorems for intrinsic volumes

## TL;DR

This paper provides concise proofs of central limit theorems for the intrinsic volumes of random polytopes within smooth convex bodies, integrating geometric estimates with probabilistic techniques.

## Contribution

It introduces simplified proofs for CLTs of intrinsic volumes using a novel combination of geometric and probabilistic methods.

## Key findings

- Central limit theorems established for intrinsic volumes
- Short and transparent proof techniques presented
- Integration of geometric estimates with Stein's method

## Abstract

Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability theory.