标题： 布朗运动流上的吉布斯测度 显示英文标题

标题： Gibbs measures on Brownian currents

摘要： 受量子场论应用的启发，我们考虑参考测度为维纳测度且相互作用由双随机积分和固定外部势能给出的吉布斯测度。 为了通过DLR方程正确表征这些测度，我们需要将维纳测度和其他对象提升到一个配置空间，在该空间中基本可观测量不仅是粒子在所有时间的位置，还包括测试向量场所做的功。 我们通过簇展开方法在小耦合区域内证明了此类吉布斯测度的存在性和基本性质。 显示英文摘要

摘要： Motivated by applications to quantum field theory we consider Gibbs measures for which the reference measure is Wiener measure and the interaction is given by a double stochastic integral and a pinning external potential. In order properly to characterize these measures through DLR equations, we are led to lift Wiener measure and other objects to a space of configurations where the basic observables are not only the position of the particle at all times but also the work done by test vector fields. We prove existence and basic properties of such Gibbs measures in the small coupling regime by means of cluster expansion.