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This article is cited in 3 scientific papers (total in 3 papers)
Combinatorial species and cluster expansions
William G. Faris Department of Mathematics, University of Arizona, Tucson, AZ, USA
Abstract:
This paper will survey recent progress on clarifying the connection between enumerative combinatorics and cluster expansions. The combinatorics side concerns species of combinatorial structures and the associated exponential generating functions. Cluster expansions, on the other hand, are supposed to give convergent expressions for measures on infinite dimensional spaces, such as those that occur in statistical mechanics. There is a dictionary between these two subjects that sheds light on each of them. In particular, it gives insight into convergence results for cluster expansions, including a well-known result of Roland Dobrushin. Furthermore, the species framework provides a context for recent results of Fernández–Procacci and of the author.
Key words and phrases:
combinatorial species, species of structures, exponential generating function, equilibrium statistical mechanics, grand partition function, cluster expansion.
Received: January 7, 2010; in revised form February 23, 2010
Citation:
William G. Faris, “Combinatorial species and cluster expansions”, Mosc. Math. J., 10:4 (2010), 713–727
Linking options:
https://www.mathnet.ru/eng/mmj400 https://www.mathnet.ru/eng/mmj/v10/i4/p713
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Abstract page: | 213 | References: | 77 |
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