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arXiv · 2303.04224

Differentiability of the Shape Function for Directed Polymers in Continuous Space

Yuri Bakhtin·Douglas Dow
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Abstract

For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension $1+1$, for positive and zero temperature, the shape function is differentiable with respect to the slope on the entire real line.

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Yuri Bakhtin, Douglas Dow. 2023-03-07. Differentiability of the Shape Function for Directed Polymers in Continuous Space. https://arxiv.org/abs/2303.04224

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