Convergence of Metropolis-Type Algorithms for a Large Canonical Ensemble

In this paper, we study the convergence of Metropolis-type algorithms used in modeling statistical systems with a variable number of particles located in a bounded volume. We justify the use of Metropolis algorithms for a particular class of such statistical systems. We prove a theorem on the geometric ergodicity of the Markov process modeling the behavior of an ensemble with a variable number of particles in a bounded volume whose interaction is described by a potential bounded below and increasing according to the law $r^{-3-\alpha}$, $\alpha\ge0$, as $r\to0$.