  We discuss the onset of symmetry breaking from the false vacuum in generic
scenarios in which the mass squared of the symmetry breaking (Higgs) field
depends linearly with time, as it occurs, via the evolution of the inflaton, in
models of hybrid inflation. We show that the Higgs fluctuations evolve from
quantum to classical during the initial stages. This justifies the subsequent
use of real-time lattice simulations to describe the fully non-perturbative and
non-linear process of symmetry breaking. The early distribution of the Higgs
field is that of a smooth classical gaussian random field, and consists of
lumps whose shape and distribution is well understood analytically. The lumps
grow with time and develop into ``bubbles'' which eventually collide among
themselves, thus populating the high momentum modes, in their way towards
thermalization at the true vacuum. With the help of some approximations we are
able to provide a quasi-analytic understanding of this process.
