Gibbs Measures on Brownian Paths
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.
KeywordsPartition Function Probability Measure Gibbs Measure Cluster Expansion Path Space
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- 1.Betz, V. and Lörinczi, J., A Gibbsian description of P(∅)1-processes, submitted for publication, 2001.Google Scholar
- 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
- 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
- 8.Simon, B.Functional Integration and Quantum PhysicsAcademic Press, 1979.Google Scholar