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In the standard Lambda cold dark matter paradigm, pure dark mattersimulations predict dwarf galaxies should inhabit dark matter haloes with acentrally diverging density `cusp'. This is in conflict with observations thattypically favour a constant density `core'. We investigate this `cusp-coreproblem' in `ultra-faint' dwarf galaxies simulated as part of the `EngineeringDwarfs at Galaxy formation's Edge' (EDGE) project. We find, similarly toprevious work, that gravitational potential fluctuations within the centralregion of the simulated dwarfs kinematically heat the dark matter particles,lowering the dwarfs' central dark matter density. However, these fluctuationsare not exclusively caused by gas inflow/outflow, but also by impulsive heatingfrom minor mergers. We use the genetic modification approach on one of ourdwarf's initial conditions to show how a delayed assembly history leads to morelate minor mergers and, correspondingly, more dark matter heating. Thisprovides a mechanism by which even ultra-faint dwarfs ($M_* <10^5\,\text{M}_{\odot}$), in which star formation was fully quenched at highredshift, can have their central dark matter density lowered over time. Incontrast, we find that late major mergers can regenerate a central dark mattercusp, if the merging galaxy had sufficiently little star formation. Thecombination of these effects leads us to predict significant stochasticity inthe central dark matter density slopes of the smallest dwarfs, driven by theirunique star formation and mass assembly histories.

EDGE: Two routes to dark matter core formation in ultra-faint dwarfs