Ruelle's probability cascades and an abstract cavity method
The so called generalized random energy model (GREM for short) has been introduced by Derrida as a very simple model in spin glass theory. Some of its remarkable properties in the limit had been discussed by Ruelle. In a joint paper with Alain-Sol Sznitman, it was found, that there is a very simple and appealing clustering process which governs some of the crucial properties of this model. This clustering process also allows to formulate a continuous version of the GREM without the necessity of cumbersome limiting procedures. Furthermore, one can give an abstract version of the so called cavity method which plays a crucial role in the nonrigorous discussion of the Sherrington-Kirkpatrick model.