Recall that the notion of
generalized function is introduced for the functions
that can not be defined pointwise, and
is given as a linear functional over the test functions.
The same idea applies to random fields. In this talk,
we study the quenched asymptotics for Brownian motion
in a generalized Gaussian field. The major ingredient
includes: Solution to
an open problem posted by Carmona and Molchanov (1995) with
an answer different from what was conjectured; the quenched
laws for Brownian motions in Newtonian-type potentials, and in the potentials
driven by white noise or by fractional white noise.