Ruelle's probability cascades seen as a fragmentation process

Abstract

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.

References in corpus (2)

• Ranked Fragmentations
• Rigorous results on some simple spin glass models

Cited by in corpus (5)

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• Spinal partitions and invariance under re-rooting of continuum random trees
• Interval partition evolutions with emigration related to the Aldous diffusion
• Fragmentation of compositions and intervals
• Different Aspects of a Model for Random Fragmentation Processes