  We discuss the use of Gaussian random fields to estimate the look-elsewhere
effect correction. We show that Gaussian random fields can be used to model the
null-hypothesis significance maps from a large set of statistical problems
commonly encountered in physics, such as template matching and likelihood ratio
tests. Some specific examples are searches for dark matter using pixel arrays,
searches for astronomical transients, and searches for fast-radio bursts.
Gaussian random fields can be sampled efficiently in the frequency domain, and
the excursion probability can be fitted with these samples to extend any
estimation of the look-elsewhere effect to lower $p$-values. We demonstrate
this using two example template matching problems. Finally, we apply this to
estimate the trial factor of a $4^3$ accelerometer array for the detection of
dark matter tracks in the Windchime project. When a global significance of
$3\sigma$ is required, the estimated trial factor for such an accelerometer
array is $10^{14}$ for a one-second search, and $10^{22}$ for a one-year
search.
