| Abstract: | The cold dark matter-based scenario is highly successful in describing large scale cosmic structure. It however faces persistent problems on (sub) galactic scales, such as the apparent overdensity of dark matter in central part of (most notably dwarf) galaxy haloes --- the so called 'cusp-core' problem. This overdensity can be reduced by 'heating' the dark matter through density (and potential) fluctuations in feedback-driven gas. I discuss a stochastic model that describes this coupling from first principles, then test its assumptions and predictions through simplified and full hydrodynamic simulations. Halo cores can also be attained by invoking ultra-light axions (of fuzzy dark matter), with the fluctuations in this case arising from the uncertainty principle. Time permitting, I will discuss their potential effects on stellar dynamics and the motion of central black holes, as predicted by the same principles used to describe the gas fluctuations.
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