Comparison between hot Jupiter hosts and a control sample of stars near the Sun. Left: The fractional rank (rank among neighbours divided by number of neighbours) in phase space density, and in residuals to the detrended phase space density, for all 198 hot Jupiter hosts. Darker symbols are stars with more neighbours in Gaia EDR3. Centre: Same, but for 600 neighbours of the Sun. Right: Histogram of the fractional residuals rank for the hot Jupiter hosts (blue for differential, orange for cumulative) and for the fractional residuals rank of 198 neighbours of the Sun chosen to have the same density fractional rank as the hot Jupiter hosts (green for differential, red for cumulative). The KS test p-value comparing the two distributions is also displayed, showing that they are statistically indistinguishable.