Uniqueness of Gibbs measures relative to Brownian motion
The existence of a Gibbs measure for a given potential follows from the existence of a ground state for the corresponding Schrödinger operator. Here, one shows that, under some mathematical conditions, this solution is unique. A first condition is related to the increase rate of the potential function, a second alternative condition is related to the ground state which is not only in \(L^{2}\) but also in \(L\).
scientific article; zbMATH DE number 1975014