Dynamic polymers: invariant measures and ordering by noise

@article{Bakhtin2021DynamicPI,
  title={Dynamic polymers: invariant measures and ordering by noise},
  author={Yuri Bakhtin and Hong-Bin Chen},
  journal={Probability Theory and Related Fields},
  year={2021}
}
We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic nearest neighbor interaction and local interaction with random environment. We prove existence and uniqueness of the solution, continuity of the flow, the order-preserving property with respect to the coordinatewise partial order, and the invariance of the… 
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