On physically large lattices, the field variables in distant regions are only weakly correlated. A single field generated by an algorithm respecting stochastic locality may therefore provide accurate stochastic estimates of the expectation values of observables with footprints much smaller than the lattice volume. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.

Theoretical Developments