  We review the idea, put forward in 1982, by Parisi and Sourlas, that the bath
of fluctuations, with which a physical system is in equilibrium, can be
resolved by the superpartners of the degrees of freedom, defined by the
classical action. This implies, in particular, that fermions can be described
in terms of their superpartners, using the Nicolai map. We focus on the
question, whether the fluctuations of scalar fields can, in fact, produce the
absolute value of the stochastic determinant itself, whose contribution to the
action can be identified with the fermionic degrees of freedom and present
evidence supporting this idea in two spacetime dimensions. The same idea leads
to a new formulation of supersymmetric QED. We also review the obstacles for
extending this approach to Yang-Mills theories and report on progress for
evading the obstructions for obtaining interacting theories in three and four
spacetime dimensions. This implies, in particular, that it is possible to
describe the effects of fermions in numerical simulations, through their
superpartners.
