  Answers to the question how a classical world emerges from underlying quantum
physics are revisited, connected and extended as follows. First, three distinct
concepts are compared: decoherence in open quantum systems,
consistent/decoherent histories and Kolmogorov consistency. Second, the crucial
role of quantum Markovianity (defined rigorously) to connect these concepts is
established. Third, using a random matrix theory model, quantum effects are
shown to be exponentially suppressed in the measurement statistics of slow and
coarse observables despite the presence of large amount of coherences. This is
also numerically exemplified, and it highlights the potential and importance of
non-integrability and chaos for the emergence of classicality.

Quantum Physics;Statistical Mechanics