Geodesic
Convergence of Metropolis-Type Algorithms for a Large Canonical Ensemble
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 519-524

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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 $r\to0$.
Keywords: Metropolis algorithm, density function, probability measure, Markov process, geometric ergodicity, drift condition.
Mots-clés : statistical ensemble 
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     author = {P. N. Vabishchevich},
     title = {Convergence of {Metropolis-Type} {Algorithms} for a {Large} {Canonical} {Ensemble}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {519--524},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a5/}
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P. N. Vabishchevich. Convergence of Metropolis-Type Algorithms for a Large Canonical Ensemble. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 519-524. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a5/