  We introduce a stochastic generalisation of the classical deterministic
Floquet-East model, a discrete circuit with the same kinetic constraint as the
East model of glasses. We prove exactly that, in the limit of long time and
large size, this model has a large deviation phase transition between active
and inactive dynamical phases. We also compute the finite time and size scaling
of general space-time fluctuations, which for the case of inactive regions
gives rise to dynamical hydrophobicity. We also discuss how, through the
Trotter limit, these exact results also hold for the continuous-time East
model, thus proving long-standing observations in kinetically constrained
models. Our results here illustrate the applicability of exact tensor network
methods for solving problems in many-body stochastic systems.
