Multispecies Virial Expansions

Abstract

We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange–Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs.

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Correspondence to Daniel Ueltschi.

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© 2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.

Communicated by H. Spohn

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Jansen, S., Tate, S.J., Tsagkarogiannis, D. et al. Multispecies Virial Expansions. Commun. Math. Phys. 330, 801–817 (2014). https://doi.org/10.1007/s00220-014-2026-9

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Keywords

  • Connected Graph
  • Formal Power Series
  • Colour Graph
  • Cluster Expansion
  • Articulation Point