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Gibbs Measures on Brownian Paths

  • József Lőrinczi
Part of the Progress in Probability book series (PRPR, volume 51)

Abstract

This is a summary of results based on recent work outlining how Gibbs measures can be defined on Brownian paths and what are their most important properties. Such Gibbs measures have a number of applications in Euclidean quantum field theory, statistical mechanics, stochastic (partial) differential equations and other areas.

Keywords

Partition Function Probability Measure Gibbs Measure Cluster Expansion Path Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Betz, V. and Lörinczi, J., A Gibbsian description of P(∅)1-processes, submitted for publication, 2001.Google Scholar
  2. 2.
    Betz, V., Hiroshima, F., LLörinczi, J., Minlos, R.A., and Spohn, H., Ground state properties of a particle coupled to a scalar quantum field, to appear in Rev. Math. Phys.(2001).Google Scholar
  3. 3.
    Hariya, Y. and Osada, H., Diffusion processes on path spaces with interactionsRev. Math. Phys.13 (2001), 199–220.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Lörinczi, J. and Minlos, R.A., Gibbs measures for Brownian paths under the effect of an external and a small pair potentialJ. Stat. Phys.105 (2001), 607–649.CrossRefGoogle Scholar
  5. 5.
    Lörinczi, J., Minlos, R.A., and Spohn, H., The infrared behaviour in Nelson’s model of a quantum particle coupled to a massless scalar field, Ann.Henri Poincaré3 (2001), 1–28.Google Scholar
  6. 6.
    Malyshev, V.A. and Minlos, R.A., Gibbs Random Fields, Kluwer Academic Publishers, 1991.CrossRefGoogle Scholar
  7. 7.
    Osada, H. and Spohn, H., Gibbs measures relative to Brownian motion, Ann.Probab.27 (1999), 1183–1207.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Simon, B.Functional Integration and Quantum PhysicsAcademic Press, 1979.Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • József Lőrinczi
    • 1
  1. 1.Zentrum MathematikTechnische Universität MünchenMünchenGermany

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