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On the correlation for Kac-like models in the convex case. (English) Zbl 0946.35508
Summary: The aim of this paper is to study the behavior as \(m\) tends to \(\infty\) of a family of measures \(\exp [ -\Phi^{(m)} (x)] dx^{(m)}\) on \(\mathbb{R}^m\), where \(\Phi^{(m)}\) is a potential on \(\mathbb{R}^m\) which is a perturbation “in a suitable sense” of the harmonic potential \(\sum_j x^2_j\).

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35B50 Maximum principles in context of PDEs
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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