For microscopically slowed-down Gaussian fields and branching Brownian motions, the recentered maximum is tight at the T^{1−α} scale, and the second-order correction exhibits a phase transition at α=1/3.
arXiv preprint arXiv:2503.17236 , year=
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Extrema of cooling branching Brownian motion and related Gaussian fields
For microscopically slowed-down Gaussian fields and branching Brownian motions, the recentered maximum is tight at the T^{1−α} scale, and the second-order correction exhibits a phase transition at α=1/3.