Cluster expansions: necessary and sufficient convergence conditions
16th March 2022, 4:00 pm – 5:00 pm
Correlation functions of Gibbs measures in general cannot be computed
explicitly, but at low density / for weak interactions they are
amenable to a power series expansion around the ideal gas (Poisson
point process). The convergence of these series has been studied at
least since the 60s, but sufficient convergence conditions keep being
developed, raising the question if there is a theoretical limit to the
improvements - an if and only if condition that cannot be surpassed.
The talk presents such an if and only if condition for repulsive
interactions. It is based on Kirkwood-Salsburg equations and
alternating sign properties and it generalizes a result by Bissacot,
Fernández and Procacci. For possibly attractive potentials, the
criterion yields new sufficient convergence conditions. Based on joint
work with Leonid Kolesnikov (arXiv:2112.13134 [math.ph]).