  We study trace estimators for equilibrium thermodynamic observables that rely
on the idea of typicality and derivatives thereof such as the
finite-temperature Lanczos method (FTLM). As numerical examples quantum spin
systems are studied. Our initial aim was to identify pathological examples or
circumstances, such as strong frustration or unusual densities of states, where
these methods could fail. Instead we failed with the attempt. All investigated
systems allow such approximations, only at temperatures of the order of the
lowest energy gap the convergence is somewhat slower in the number of random
vectors over which observables are averaged.
