Graphical constraints for non-equilibrium Markov processes
Undirected graphical models is intimately connected to equilibrium statistical mechanics with (graphical) Gibbs measures as steady-state distributions, and with the graphical constraints inducing conditional independencies of the steady-state distributions. However, many Markov processes have dynamics with natural graphical constraints, yet their steady-state distributions are not Gibbs measures and may have no non-trivial conditional independencies. These processes have asymmetric dynamics, they do not satisfy detailed balance, and the constraints are captured by directed graphs. In the talk I will outline some first steps towards understanding how these directed graphs entail constraints on the cumulant tensors of the steady-state distributions.