# Stochastic Inflation and Primordial Black Holes

In the inflationary paradigm, the transition from quantum fluctuations to classical but stochastic density perturbations plays an important role. In particular, it implies that the open quantum system comprising the super-Hubble degrees of freedom can be described with a classical stochastic theory, the “stochastic inflation” formalism. In this framework, the short-wavelength quantum fluctuations act as a classical noise on the dynamics of the super-Hubble scales.