The maximal action A satisfies A = a ln L + O(1) with overwhelming probability for a deterministic a in (0, ∞).
On minimizing curves in a Brownian potential.Probability Theory and Related Fields, 1–62 (2026), Springer
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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, ∞).