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Multispecies Virial Expansions

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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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Authors and Affiliations

  1. Leiden University, Postbus 9512, 2300 RA, Leiden, The Netherlands

    Sabine Jansen

  2. Department of Mathematics, University of Warwick, Coventry, CV4 7AL, UK

    Stephen J. Tate & Daniel Ueltschi

  3. Department of Applied Mathematics, University of Crete, P.O. Box 2208, 71003, Heraklion, Greece

    Dimitrios Tsagkarogiannis

Authors
  1. Sabine Jansen
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  2. Stephen J. Tate
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  3. Dimitrios Tsagkarogiannis
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  4. Daniel Ueltschi
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Correspondence to Daniel Ueltschi.

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Communicated by H. Spohn

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

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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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  • DOI: https://doi.org/10.1007/s00220-014-2026-9

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