  The 'Neumann-Ulam' Monte-Carlo sampling is described for the calculation of a
matrix inversion or a Green function in case of Hubbard-Stratonovich
(HS-)transformed coherent state path integrals. We illustrate how to circumvent
direct numerical inversion of a matrix to its Green function by taking random
walks of suitably chosen matrices within a path integral of even- and
complex-valued self-energy matrices. The application of a random walk sampling
is given by the possible separation of the total matrix, e.g. that matrix which
determines the Green function from its inversion, into a part of unity minus
(or plus) a matrix which only contains eigenvalues with absolute value smaller
than one. This allows to expand the prevailing Green function around the unit
matrix in a Taylor expansion with a separated, special matrix of sufficiently
small eigenvalues. The presented sampling method is particularly appropriate
around the saddle point solution of the self-energy in a sigma model by using
random number generators. It is also capable for random sampling of
HS-transformed path integrals from fermionic fields which interact through
gauge invariant bosons according to Yang-Mills theories.
