Yuri Bakhtin, Douglas Dow
Published 2023-03-07, updated 2023-03-16Version 2
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.
Comments: Minor changes in this version, adding a couple remarks and correcting a few typos. 28 pages
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