Ruelle's Probability Cascades Seen as a Fragmentation Process

A.-L. Basdevant

2006, v.12, №3, 447-474

ABSTRACT

In this paper, we study Ruelle's probability cascades [D. Ruelle, A mathematical reformulation of Derrida's REM and GREM. Commun. Math. Phys., 1987, v. 108, 225-239] 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 large times of Ruelle's fragmentation process.

Keywords: fragmentation,exchangeable partition,Ruelle's cascades

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