Existence of Gibbs measures relative to Brownian motion

Details Existence of Gibbs measures relative to Brownian motion Existence of Gibbs measures relative to Brownian motion

2001-07-25

arxiv.org/abs/math/0107184v1

Mathematics

Probability

17 pages

Scientific paper

We prove existence of infinite volume Gibbs measures relative to Brownian motion. We require the pair potential W to fulfill a uniform integrability condition, but otherwise our restrictions on the potentials are relatively weak. In particular, our results are applicable to the massless Nelson model. We also prove an upper bound for path fluctuations under the infinite volume Gibbs measures.

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