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

April, 2001
Report Number: 
592
Authors: 
Persi Diaconis & Steven N. Evans
Citation: 
S{\'e}minaire Lotharingien de Combinatoire, Issue 46, (45 pp.) 2001
Abstract: 

We study a class of Gaussian random fields with negative correlations. These fields are easy to simulate. They are defined in a natural way from a Markov chain that has the index space of the Gaussian field as its state space. In parallel with Dynkin's investigation of Gaussian fields 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 field. Our interest in such fields was initiated by their appearance in random matrix theory.

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