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Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem. (English) Zbl 1126.44007
The authors try to show that a large connection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to an infinite exchangeable process. A solution to a new moment problem is also suggested.

MSC:
44A60 Moment problems
60G09 Exchangeability for stochastic processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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