On Ruelle's Probability Cascades and an Abstract Cavity Method
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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- October 1998
- DOI:
- 10.1007/s002200050450
- Bibcode:
- 1998CMaPh.197..247B
- Keywords:
-
- Equivalence Class;
- Markov Process;
- Cluster Process;
- Continuous Probability;
- Cavity Method