  We extend previous work on the numerical diagonalization of quantum stress
tensor operators in the Minkowski vacuum state, which considered operators
averaged in a finite time interval, to operators averaged in a finite spacetime
region. Since real experiments occur over finite volumes and durations,
physically meaningful fluctuations may be obtained from stress tensor operators
averaged by compactly supported sampling functions in space and time. The
direct diagonalization, via a Bogoliubov transformation, gives the eigenvalues
and the probabilities of measuring those eigenvalues in the vacuum state, from
which the underlying probability distribution can be constructed. For the
normal-ordered square of the time derivative of a massless scalar field in a
spherical cavity with finite degrees of freedom, analysis of the tails of these
distributions confirms previous results based on the analytical treatment of
the high moments. We find that the probability of large vacuum fluctuations is
reduced when spatial averaging is included, but the tail still decreases more
slowly than exponentially as the magnitude of the measured eigenvalues
increases, suggesting vacuum fluctuations may not always be subdominant to
thermal fluctuations and opening up the possibility of experimental observation
under the right conditions.
