  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.
