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.
Convergence of solutions of the Kolmogorov equation to travelling waves
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Quenched random growth rates make FKPP fronts travel faster on average by a universal factor times the disorder variance and produce diffusive position fluctuations whose strength also scales with the square of the variance.
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FKPP fronts in quenched random media
Quenched random growth rates make FKPP fronts travel faster on average by a universal factor times the disorder variance and produce diffusive position fluctuations whose strength also scales with the square of the variance.