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On Ruelle's Probability Cascades and an Abstract Cavity Method

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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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Authors and Affiliations

  1. Angewandte Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland, , , , , , CH

    E. Bolthausen

  2. Departement Mathematik, ETH-Zürich, CH-8092 Zürich, Switzerland, , , , , , CH

    A.-S. Sznitman

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  1. E. Bolthausen
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  2. A.-S. Sznitman
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Received: 6 October 1997 / Accepted: 2 March 1998

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Bolthausen, E., Sznitman, AS. On Ruelle's Probability Cascades and an Abstract Cavity Method. Comm Math Phys 197, 247–276 (1998). https://doi.org/10.1007/s002200050450

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  • DOI: https://doi.org/10.1007/s002200050450

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