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Exact asymptotics in a mean field model with random potential
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  • Published: June 1990

Exact asymptotics in a mean field model with random potential

  • Klaus Fleischmann1 &
  • Stanislav Alekseevich Molchanov2 

Probability Theory and Related Fields volume 86, pages 239–251 (1990)Cite this article

Summary

For a mean field operator with a random potential, asymptotic properties of the eigenvalues and eigenfunctions are studied and applied to investigate the longerm behavior of the solutions of a corresponding large system of differential equations. The total mass of the system is approximately concentrated in the record point of the random potential (complete localization). A more detailed inspection of the peaks shows that there is a phase transition: Only in the case of a moderate increase of time relatively to the growth of the space size the model behaves similarly to the system without “diffusion”. But also in the non-moderate case the asymptotic height of peaks can exactly be described.

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Author information

Authors and Affiliations

  1. Karl Weierstrass Institute of Mathematics, Academy of Sciences of the GDR, DDR-1086, Berlin, German Democratic Republic

    Klaus Fleischmann

  2. Faculty of Mechanics and Mathematics, Moscow State University, SU-117234, Moscow, USSR

    Stanislav Alekseevich Molchanov

Authors
  1. Klaus Fleischmann
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  2. Stanislav Alekseevich Molchanov
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Cite this article

Fleischmann, K., Molchanov, S.A. Exact asymptotics in a mean field model with random potential. Probab. Th. Rel. Fields 86, 239–251 (1990). https://doi.org/10.1007/BF01474644

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  • Received: 06 October 1988

  • Revised: 14 February 1989

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01474644

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Keywords

  • Differential Equation
  • Phase Transition
  • Stochastic Process
  • Probability Theory
  • Field Operator
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