A different construction of Gaussian fields from Markov chains: Dirichlet covariances

Abstract. We study a class of Gaussian random elds with negative correlations. These elds are easy to simulate. They are de ned in a natural way from a Markov chain that has the index space of the Gaussian eld as its state space. In parallel with Dynkin's investigation of Gaussian elds having covariance given by the Green's function of a Markov process, we develop connections between the occupation times of the Markov chain and the prediction properties of the Gaussian eld. Our interest in such eldswas initiated by their appearance in random matrix theory. 1