We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the
Boltzmann-Grad limit. We prove that (1) fluctuations of the empirical measure from the …

We prove that a Gibbs point process interacting via a finite-range, repulsive potential ϕ
exhibits a strong spatial mixing property for activities λ< e/Δ ϕ, where Δ ϕ is the potential …

We prove absolute convergence of the multi-body correlation functions as a power series in
the density uniformly in their arguments. This is done by working in the context of the cluster …

A generalized version of Groeneveld's convergence criterion for the virial expansion and
generating functionals for weighted two-connected graphs is proven. This criterion works for …

We consider a one-dimensional lattice system of unbounded, real-valued spins with
arbitrary strong, quadratic, finite-range interaction. We show the equivalence of correlations …

We prove the existence of a liquid-gas phase transition for continuous Gibbs point process
in $\mathbb {R}^ d $ with Quermass interaction. The Hamiltonian we consider is a linear …

We review some recent progress on applications of Cluster Expansions. We focus on a
system of classical particles living in a continuous medium and interacting via a stable and …

We show the validity of the cluster expansion in the canonical ensemble for the Ising model.
We compare the lower bound of its radius of convergence with the one computed by the …

We consider a system of classical particles confined in a box\varLambda ⊂ R^ d Λ⊂ R d
with zero boundary conditions interacting via a stable and regular pair potential. Based on …

The theory of phase transitions is one of the branches of statistical physics in which
smoothness and continuity play an important role. In fact, phase transitions are …