A. L. Rebenko

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Articles: 8

An exponential representation for some integrals with respect to Lebesgue-Poisson measure

V. A. Boluh, A. L. Rebenko

↓ Abstract   |   Article (.pdf)

MFAT 20 (2014), no. 2, 186-192


We prove a theorem that allows to simplify some combinatorial calculations. An example of application of this theorem in statistical mechanics is given.

On stability, superstability and strong superstability of classical systems of statistical mechanics

A. L. Rebenko, M. V. Tertychnyi

↓ Abstract   |   Article (.pdf)

MFAT 14 (2008), no. 3, 287-296


A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. We give a connection between conditions of superstability (strong superstability) and the problem of minimization of Riesz energy in bounded volumes.

Superstable criterion and superstable bounds for infinite range interaction I: two-body potentials

S. N. Petrenko, A. L. Rebenko

↓ Abstract   |   Article (.pdf)

MFAT 13 (2007), no. 1, 50-61


A continuous infinite system of point particles interacting via two-body infinite-range potential is considered in the framework of classical statistical mecha ics. We propose some new criterion for interaction potentials to be superstable and give a very transparent proof of the Ruelle's uniform bounds for a family of finite volume correlation functions. It gives a possibility to prove that for any temperature and chemical activity there exists at least one Gibbs state. This article is a generalization of the work \cite{Re98} for the case of infinite range interaction potential.

Polymer expansions for continuous classical systems with many-body interaction

Alexei L. Rebenko

MFAT 11 (2005), no. 1, 73-87


Euclidean Gibbs states for quantum continuous systems via cluster expansion. II. Bose and Fermi statistics

Alexei L. Rebenko

MFAT 5 (1999), no. 2, 86-100


Euclidean Gibbs states for quantum continuous systems with Boltzmann statistics via cluster expansion

Yu. G. Kondratiev, A. L. Rebenko, M. Röckner, M. Röckner, G. V. Shchepanʹuk

MFAT 3 (1997), no. 1, 62-81


Cluster expansions of Brydges-Federbush type for quantum lattice systems

A. Yu. Kondratiev, A. L. Rebenko

MFAT 2 (1996), no. 3, 59-68


Some remarks about cluster expansion for unbounded continuous spin systems in quantum statistical mechanics

Alexei Yu. Kondratiev, Alexei L. Rebenko

MFAT 2 (1996), no. 2, 61-69


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