Gibbs Measures on Brownian Paths: Theory and Applications

Volker Betz, József Lőrinczi and Herbert Spohn
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Volker Betz: Technische Universität München, Zentrum Mathematik
József Lőrinczi: Technische Universität München, Zentrum Mathematik
Herbert Spohn: Technische Universität München, Zentrum Mathematik

A chapter in Interacting Stochastic Systems, 2005, pp 75-102 from Springer

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.

Keywords: Brownian Motion; Central Limit Theorem; Gibbs Measure; Cluster Expansion; Path Space (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-27110-9_5

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DOI: 10.1007/3-540-27110-4_5

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