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On Ruelle's Probability Cascades and an Abstract Cavity Method

Authors
  • Bolthausen, E.1
  • Sznitman, A.-S.2
  • 1 Angewandte Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland, CH
  • 2 Departement Mathematik, ETH-Zürich, CH-8092 Zürich, Switzerland, CH
Type
Published Article
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Publication Date
Oct 01, 1998
Volume
197
Issue
2
Pages
247–276
Identifiers
DOI: 10.1007/s002200050450
Source
Springer Nature
Keywords
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Abstract

We construct in this work a Markov process which describes a clustering mechanism through which equivalence classes on ℕ are progressively lumped together. This clustering process gives a new description of Ruelle's continuous probability cascades. It also enables to introduce an abstract cavity method, which mimicks certain features of the cavity method developed by physicists in the context of the Sherrington Kirkpatrick model.

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