The maximal action A satisfies A = a ln L + O(1) with overwhelming probability for a deterministic a in (0, ∞).
On optimal matchings.Combina- torica,4, 4, 259–264 (1984), Springer-Verlag Berlin/Heidelberg
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Quantitative homogenization of the maximal action of curves in a Brownian potential
The maximal action A satisfies A = a ln L + O(1) with overwhelming probability for a deterministic a in (0, ∞).