Existence of limiting correlation functions and their cluster representation

08.04.2019, 12:00  –  Golm, Haus 9, Raum 0.13
Forschungsseminar Wahrscheinlichkeitstheorie

Suren Poghosyan (Yerevan, Armenia)

The traditional method for the construction of the limiting Gibbs measure uses the thermodynamic limit of the finite volume correlation functions. These limiting correlation functions are defined implicitly as a solution of a system of linear integral equations of Kirkwood-Salzburg type.

We present an alternative approach based on a representation of both finite volume and limiting correlation functions via the same function which permits efficient bounds in terms of special graphs called forests. In particular we get a convergent expansion of the limiting correlation functions in powers of the activity.