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.
Activated Aging Dynamics and Effective Trap Model Description in the Random Energy Model
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abstract
We study the out-of-equilibrium aging dynamics of the Random Energy Model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second.
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2024 1verdicts
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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.