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Borel summation of Brydges-Federbush-Mayer expansions for multiparticle potentials

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Abstract

We study the structure of Brydges-Federbush-Mayer expansions (BFME) for M-particle interactions of continuous systems of classical statistical mechanics. We derive estimates on the number of trees and the sums of their contributions and prove the Borel summability of expansions. We prove the convergence of BFME in the case of certain three-particle potentials.

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Literature cited

  1. W. Greenberg, “Thermodynamic states of classical systems,” Commun. Math. Phys.,22, 259–268 (1971).

    Google Scholar 

  2. M. Duneau and B. Souillard, “Cluster properties of lattice and continuous systems,” Commun. Math. Phys.,47, 155–166 (1976).

    Google Scholar 

  3. M. Duneau, B. Souillard, and D. Iagolnitzer, “Decay of correlations for infinite-range interactions,” J. Math. Phys.,16, 1662–1664 (1975).

    Google Scholar 

  4. D. Brydges and P. Federbush, “A new form of the Mayer expansion in classical statistical mechanics,” J. Math. Phys.,19, 2064–2067 (1978).

    Google Scholar 

  5. D. Brydges, “A short course of cluster expansions,” Les Houches, Session XLIII, K. Osterwalder and R. Stora (eds.) (1984).

  6. A. L. Rebenko, “Mathematical foundations of equilibrium classical statistical mechanics of charged particles,” Russ. Math. Surveys,43, No. 3, 65–116 (1988).

    Google Scholar 

  7. G. A. Battle and P. Federbush, “A note on cluster expansions, tree-graph identities, extra 1/N! factors,” Lett. Math. Phys.,8, 55–57 (1984).

    Google Scholar 

  8. G. A. Battle, “A new combinatoric estimate for cluster expansions,” Commun. Math. Phys.,94, 133–139 (1984).

    Google Scholar 

  9. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, New York-London (1972).

    Google Scholar 

  10. V. I. Skrypnik, “Correlation functions of infinite system of interacting brownian particles. Local in time evolution close to equilibrium,” J. Statis. Phys.,38, 587–602 (1984).

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev

    A. L. Rebenko & P. V. Reznichenko

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  1. A. L. Rebenko
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  2. P. V. Reznichenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 648–657, May, 1991.

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Rebenko, A.L., Reznichenko, P.V. Borel summation of Brydges-Federbush-Mayer expansions for multiparticle potentials. Ukr Math J 43, 601–609 (1991). https://doi.org/10.1007/BF01058547

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  • DOI: https://doi.org/10.1007/BF01058547

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