# A. L. Rebenko

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

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **11** (2005), no. 1, 73-87

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

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **3** (1997), no. 1, 62-81

### Cluster expansions of Brydges-Federbush type for quantum lattice systems

A. Yu. Kondratiev, A. L. Rebenko

Methods Funct. Anal. Topology **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

Methods Funct. Anal. Topology **2** (1996), no. 2, 61-69