Under OU-GFF dynamics thickness evolves continuously for all points and realizes every deterministic function; under stationary SHE dynamics thickness is discontinuous, super-thick points appear, and there exist phase transitions at gamma squared values 8, 6, 16/3, ... converging to 4 that match Ber
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Thick points under Gaussian free field dynamics
Under OU-GFF dynamics thickness evolves continuously for all points and realizes every deterministic function; under stationary SHE dynamics thickness is discontinuous, super-thick points appear, and there exist phase transitions at gamma squared values 8, 6, 16/3, ... converging to 4 that match Ber