Existence of Gibbs Measures Relative to Brownian Motion,

#### V. Betz

2003, v.9, Issue 1, 85-102

ABSTRACT

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.

Keywords: stationary non-Markov processes,Gibbs measures,Nelson model