Penrose-Stable Interactions in Classical Statistical Mechanics

Gibbs point processes on path space: existence, cluster expansion and uniqueness

“…For the second statement, consider = {x 1 , … , x }. It is known (see [15], Lemmas 12 and 15), that the limiting correlation functional ( ) ( ) coincides with the correlation function ( ) ( ) whenever the expression in ( 14) is well de ned. As this is true thanks to (14), the Ruelle bound (29) holds for any ∈ G , ( ).…”

“…Indeed, S. Poghosyan and D. Ueltschi develop, in [14], abstract techniques that can be used both in the classical and in the marked setting, under assumptions of socalled modi ed-regularity of the interaction. These assumptions and techniques are further developed in [15] by S. Poghosyan and H. Zessin, proving uniqueness of in nite-volume Gibbs point processes for potentials satisfying a certain stability condition (which they refer to as Penrose stability). Some similar result is presented by S. Jansen in [3], but making strong use of the repulsive nature of the interaction she considers.…”