  JWST is unveiling a surprising lack of evolution in the number densities of
ultraviolet-selected (UV) galaxies at redshift $z\gtrsim 10$. At the same time,
observations and simulations are providing evidence for highly bursty star
formation in high-$z$ galaxies, resulting in significant scatter in their UV
luminosities. Galaxies in low-mass dark matter halos are expected to experience
most stochasticity due to their shallow potential wells. Here, we explore the
impact of a mass-dependent stochasticity using a simple analytical model. We
assume that scatter in the $M_\mathrm{UV}-M_h$ relation increases towards lower
halo masses, following the decrease in halo escape velocity,
$\sigma_\mathrm{UV} \sim M_h^{-1/3}$, independent of redshift. Since low-mass
halos are more dominant in the early universe, this model naturally predicts an
increase in UV luminosity functions (LFs) at high redshifts compared to models
without scatter. We make predictions for additional observables which would be
affected by stochasticity and could be used to constrain its amplitude,
finding: (i) galaxies are less clustered compared to the no-scatter scenario,
with the difference increasing at higher-$z$; (ii) assuming star-bursting
galaxies dominate the ionizing photon budget implies reionization starts
earlier and is more gradual compared to the no-scatter case, (iii) at fixed UV
magnitude galaxies should exhibit wide ranges of UV slopes, nebular emission
line strengths and Balmer breaks. Comparing to observations, the mass-dependent
stochasticity model successfully reproduces the observed LFs up to $z\sim12$.
However, the model cannot match the observed $z\sim14$ LFs, implying additional
physical processes enhance star formation efficiency in the earliest galaxies.
