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Gibbs Measures on Brownian Paths: Theory and Applications

In: Interacting Stochastic Systems

Author

Listed:
  • Volker Betz

    (Technische Universität München, Zentrum Mathematik
    GSF Forschungszentrum, Institute for Biomathematics and Biometry)

  • József Lőrinczi

    (Technische Universität München, Zentrum Mathematik)

  • Herbert Spohn

    (Technische Universität München, Zentrum Mathematik)

Abstract

Summary We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when the energy only depends on increments, we present a functional central limit theorem. We also explain connections with other work and state open problems of interest.

Suggested Citation

  • Volker Betz & József Lőrinczi & Herbert Spohn, 2005. "Gibbs Measures on Brownian Paths: Theory and Applications," Springer Books, in: Jean-Dominique Deuschel & Andreas Greven (ed.), Interacting Stochastic Systems, pages 75-102, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27110-9_5
    DOI: 10.1007/3-540-27110-4_5
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