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math.PR2023
Differentiability of the effective Lagrangian for Hamilton-Jacobi-Bellman equations in dynamic random environments
Yuri Bakhtin, Douglas Dow
We prove differentiability of the effective Lagrangian for continuous time multidimensional directed variational problems in random dynamic environments with positive dependence ra…
math.PR2023
Differentiability of the Shape Function for Directed Polymers in Continuous Space
Yuri Bakhtin, Douglas Dow
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 mo…