Non-uniqueness of Gibbs measures relative to Brownian motion
نویسندگان
چکیده
We consider Gibbs measures relative to Brownian motion of Feynman-Kac type, with single site potential V . We show that for a large class of V , including the Coulomb potential, there exist infinitely many infinite volume Gibbs measures.
منابع مشابه
Gibbs measures on Brownian paths: Theory and applications
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.
متن کاملGibbs Measures Relative to Brownian Motion
We consider Brownian motion perturbed by the exponential of an action. The action is the sum of an external, one-body potential and a two-body interaction potential which depends only on the increments. Under suitable conditions on these potentials we establish existence and uniqueness of the corresponding Gibbs measure. We also provide an example where uniqueness fails because of a slow decay ...
متن کاملUniqueness of Gibbs measures relative to Brownian motion
We consider the set of Gibbs measures relative to Brownian motion for given potential V . V is assumed to be Kato-decomposable but general otherwise. A Gibbs measure for such a potential is in many cases given by a reversible Itô diffusion μ. We show that if V is growing at infinity faster than quadratically and in a sufficiently regular way, then μ is the only Gibbs measure that exists. For ge...
متن کاملExistence of Gibbs measures relative to Brownian motion
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.
متن کاملGibbs Measures for Brownian Paths under the Eeect of an External and a Small Pair Potential
We consider Brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a Gibbs measure. Uniqueness of the Gibbs measure for two cases is shown. Also the typical path behaviour and some further properties are derived. We use cluster expansion in the small coupling parameter.
متن کامل