  In this work we present a detailed study of the Fermion Monte Carlo algorithm
(FMC), a recently proposed stochastic method for calculating fermionic
ground-state energies [M.H. Kalos and F. Pederiva, Phys. Rev. Lett. vol. 85,
3547 (2000)]. A proof that the FMC method is an exact method is given. In this
work the stability of the method is related to the difference between the
lowest (bosonic-type) eigenvalue of the FMC diffusion operator and the exact
fermi energy. It is shown that within a FMC framework the lowest eigenvalue of
the new diffusion operator is no longer the bosonic ground-state eigenvalue as
in standard exact Diffusion Monte Carlo (DMC) schemes but a modified value
which is strictly greater. Accordingly, FMC can be viewed as an exact DMC
method built from a correlated diffusion process having a reduced Bose-Fermi
gap. As a consequence, the FMC method is more stable than any transient method
(or nodal release-type approaches). We illustrate the various ideas presented
in this work with calculations performed on a very simple model having only
nine states but a full sign problem. Already for this toy model it is clearly
seen that FMC calculations are inherently uncontrolled.
