Proves second-order asymptotics for maximal displacement in time-inhomogeneous N-particle branching Brownian motion with a transition at log N ≈ T^{1/3}, recovering Brunet-Derrida behavior when log N ≪ T^{1/3}, and interprets results as beam search efficiency on CREM around its hardness threshold.
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Time-inhomogeneous N-particle Branching Brownian Motion and the continuous random energy model
Proves second-order asymptotics for maximal displacement in time-inhomogeneous N-particle branching Brownian motion with a transition at log N ≈ T^{1/3}, recovering Brunet-Derrida behavior when log N ≪ T^{1/3}, and interprets results as beam search efficiency on CREM around its hardness threshold.