On trees with finite linear branches, there exist universal harmonic functions whose boundary martingale sequences are dense in the space of measurable functions, and frequently universal ones visit every open set with positive lower density.
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Frequently dense harmonic functions and universal martingales on trees
On trees with finite linear branches, there exist universal harmonic functions whose boundary martingale sequences are dense in the space of measurable functions, and frequently universal ones visit every open set with positive lower density.