A central limit theorem for conservative fragmentation chains

Abstract

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\varepsilon$ ( $\varepsilon>0$ ). It is known (Bertoin and Martínez, 2005) that the empirical measure of these fragments converges in law, under some renormalization. Hoffmann and Krell (2011) showed a bound for the rate of convergence. Here, we show a central limit theorem, under some assumptions. This gives us an exact rate of convergence.