Maslov's complex germ and the asymptotic formula for the Gibbs canonical distribution (Q1290803)

The author studies an \(N\)-particle system following a Gibbs canonical distribution given in terms of a Hamilton function. The external potential is \({\mathcal O}(1)\), the potential of pairwise interaction is \({\mathcal O}(1/N)\), the potential of triple interaction is \({\mathcal O} (1/N^2)\) and so on. The author investigates the asymptotics of the free energy and of the partition function as the number \(N\) of particles tends to infinity. An explicit formula is given, which enables the author to prove that the chaos property holds for \(k\)-particle distributions \((k\) is fixed) and not for the \(N\)-particle distribution.