Plancherel random trees have height H_n satisfying H_n / log n converging in probability to an explicit constant c_star(2) characterized variationally via branching random walk.
Shi.Branching Random Walks - École d’été de probabilités de Saint-Flour XLII - 2012, volume 2151 of Lecture Notes in Mathematics
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Asymptotic height of Plancherel random trees
Plancherel random trees have height H_n satisfying H_n / log n converging in probability to an explicit constant c_star(2) characterized variationally via branching random walk.