Stochastic Split Determinant Algorithms

I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the determinant through local loop action, and the idea of treating the infrared part of the split through explicit diagonalizations. I suggest that exact algorithms of practical relevance might be based on the Markov processes so constructed.