  Single-propagator traces are the most elementary fermion Wick contractions
which occur in numerical lattice QCD, and are usually computed by introducing
random-noise estimators to profit from volume averaging. The additional
contribution to the variance induced by the random noise is typically orders of
magnitude larger than the one due to the gauge field. We propose a new family
of stochastic estimators of single-propagator traces built upon a frequency
splitting combined with a hopping expansion of the quark propagator, and test
their efficiency in two-flavour QCD with pions as light as 190 MeV. Depending
on the fermion bilinear considered, the cost of computing these diagrams is
reduced by one to two orders of magnitude or more with respect to standard
random-noise estimators. As two concrete examples of physics applications, we
compute the disconnected contributions to correlation functions of two vector
currents in the isosinglet omega channel and to the hadronic vacuum
polarization relevant for the muon anomalous magnetic moment. In both cases,
estimators with variances dominated by the gauge noise are computed with a
modest numerical effort. Theory suggests large gains for disconnected three and
higher point correlation functions as well. The frequency-splitting estimators
and their split-even components are directly applicable to the newly proposed
multi-level integration in the presence of fermions.
