On Ruelle’s probability cascades and an abstract cavity method. (English) Zbl 0927.60071

From the authors’ abstract: It is constructed 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.


60J25 Continuous-time Markov processes on general state spaces
60K10 Applications of renewal theory (reliability, demand theory, etc.)
Full Text: DOI