Ruelle's probability cascades seen as a fragmentation process

In this paper, we study Ruelle's probability cascades in the framework of time-inhomogeneous fragmentation processes. We describe Ruelle's cascades mechanism exhibiting a family of measures $(\nu_t,t\in [0,1[)$ that characterizes its infinitesimal evolution. To this end, we will first extend the time-homogeneous fragmentation theory to the inhomogeneous case. In the last section, we will study the behavior for small and large times of Ruelle's fragmentation process