Where do High-Velocity Dark Matter Particles come from in the Milky Way?

High-velocity particles ( $v>v_{\mathrm{e}\mathrm{s}\mathrm{c}}$) in the Milky Way are rare but nonetheless important to characterize due to their impact on dark matter (DM) direct detection experiments. We select halos similar in mass to the Milky Way in a large-volume dark matter simulation and measure the incidence of high-velocity particles, finding that an average fraction $\sim 1.3\times {10}^{-5}$ of the DM particles have $\mathrm{\Delta }v>600$ km/s within 5-11 kpc of the halo centers. However, some systems have dramatically higher fractions. Milky Way-like systems with high-speed satellites can have high-velocity DM fractions of order $\sim 100\times$ higher than average. The environment also affects high-velocity DM fractions; massive nearby halos ( $>{10}^{13}{M}_{\odot }$) can boost high-velocity DM density by $\sim 10\times$, although there is little effect for nearby Andromeda-like systems. We confirm previous predictions from zoom-in simulations that the high-velocity particles in the Milky Way with heliocentric speeds $>700$ km/s primarily originate from the Large Magellanic Cloud, and provide a table of expected high-velocity DM densities at different heliocentric velocity thresholds.