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Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres

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Abstract

We consider the stochastic dynamics that is the Boltzmann-Grad limit of the Hamiltonian dynamics of a system of hard spheres. A new concept of averages over states of stochastic systems is introduced, in which the contribution of the hypersurfaces on which stochastic point particles interact is taken into account. We give a rigorous derivation of the infinitesimal operators of semigroups of evolution operators.

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References

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Authors and Affiliations

  1. Politecnico di Milano, Italy

    M. Lampis

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    D. Ya. Petrina & K. D. Petrina

Authors
  1. M. Lampis
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  2. D. Ya. Petrina
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  3. K. D. Petrina
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Additional information

Published in Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 614–635, May, 1999

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Lampis, M., Petrina, D.Y. & Petrina, K.D. Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres. Ukr Math J 51, 684–706 (1999). https://doi.org/10.1007/BF02591705

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  • DOI: https://doi.org/10.1007/BF02591705

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