In the infinite-dimensional limit the elastic polymer free energy is given explicitly by the law of the inner product of two independent paths; the model is diffusive for short-range or weak correlations and superdiffusive for strong long-range correlations, with the transition coinciding exactly to
Minimal surfaces in random environment.arXiv preprint2401.06768
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The maximal action A satisfies A = a ln L + O(1) with overwhelming probability for a deterministic a in (0, ∞).
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Wandering Exponents and the Free Energy of the High-Dimensional Elastic Polymer
In the infinite-dimensional limit the elastic polymer free energy is given explicitly by the law of the inner product of two independent paths; the model is diffusive for short-range or weak correlations and superdiffusive for strong long-range correlations, with the transition coinciding exactly to
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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, ∞).