DLR measures for one-dimensional harmonic systems

Summary A one-dimensional chain of nearest neighbor linearly interacting oscillators {q_x}_x is studied. The set of all its extremal DLR measures is characterized in terms of a parameter ². For each there is a Gaussian DLR measure with support on the set of configurations determined by the rate of growth of¦q_x¦. It is then finally proved that there is only one translationally invariant DLR measure. This proves the following conjecture: invariant DLR measures give uniformly finite first moment to ¦q_x¦.