A large population of extended substructures generates a stochastic gravitational field that is fully specified by the function $p({bf F})$, which defines the probability that a tracer particle experiences a force $bf F$ within the interval ${bf F},{bf F}+ dbf F$. This paper presents a statistical technique for deriving the spectrum of random fluctuations directly from the number density of substructures with known mass and size functions. Application to the subhalo population found in cold dark matter simulations of Milky Way-sized haloes shows that, while the combined force distribution is governed by the most massive satellites, the fluctuations of the {it tidal} field are completely dominated by the smallest and most abundant subhaloes. In light of this result we discuss observational experiments that may be sufficiently sensitive to Galactic tidal fluctuations to probe the dark low-end of the subhalo mass function and constrain the particle mass of warm and ultra-light axion dark matter models.
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