# Central-limit theorem for conservative fragmentation chains

## TL;DR

This paper establishes a central-limit theorem for the empirical measure of fragments in a conservative fragmentation process, extending previous convergence results and providing insights into the distributional fluctuations of small fragments.

## Contribution

It introduces a central-limit theorem for the empirical measure of fragments in a conservative fragmentation chain, under specific assumptions, advancing the understanding of their probabilistic behavior.

## Key findings

- Proves a central-limit theorem for the empirical measure of fragments
- Provides bounds on the rate of convergence in fragmentation processes
- Enhances understanding of fluctuations in fragment sizes

## Abstract

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\epsilon$ ($\epsilon$ > 0). Is is known ([BM05]) that the empirical measure of these fragments converges in law, under some renormalization. In [HK11], the authors show a bound for the rate of convergence. Here, we show a central-limit theorem, under some assumptions.