The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up opportunity investigate probabilistic machine learning within theory. Here, we will discuss how discretized theories, such as $\phi^{4}$ lattice theory a square lattice, are mathematically equivalent Markov fields, notable class graphical models with applications in vari...

– 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 occup...