  Cavity point-to-set correlations are real-space tools to detect the
roughening of the free-energy landscape that accompanies the dynamical slowdown
of glass-forming liquids. Measuring these correlations in model glass formers
remains, however, a major computational challenge. Here, we develop a general
parallel-tempering method that provides orders-of-magnitude improvement for
sampling and equilibrating configurations within cavities. We apply this
improved scheme to the canonical Kob-Andersen binary Lennard-Jones model for
temperatures down to the mode-coupling theory crossover. Most significant
improvements are noted for small cavities, which have thus far been the most
difficult to study. This methodological advance also enables us to study a
broader range of physical observables associated with thermodynamic
fluctuations. We measure the probability distribution of overlap fluctuations
in cavities, which displays a non-trivial temperature evolution. The
corresponding overlap susceptibility is found to provide a robust quantitative
estimate of the point-to-set length scale requiring no fitting. By resolving
spatial fluctuations of the overlap in the cavity, we also obtain quantitative
information about the geometry of overlap fluctuations. We can thus examine in
detail how the penetration length as well as its fluctuations evolve with
temperature and cavity size.
