  The statics of the Fredrickson-Andersen model (FAM) of the liquid-glass
transition is solved on the Bethe lattice (BL). The kinetic constraints of the
FAM imply on the BL an ergodicity-breaking transition to a (glassy) phase where
a fraction of spins of the system is permanently blocked, and the remaining
"free" spins become non-trivially correlated. We compute several observables of
the ergodicity-broken phase, such as the self-overlap, the configurational
entropy and the spin-glass susceptibility, and we compare the analytical
predictions with numerical experiments. The cavity equations that we obtain
allow to define algorithms for fast equilibration and accelerated dynamics. We
find that at variance with spin-glass models, the correlations inside a state
do not exhibit a critical behavior.
