• Corpus ID: 238857063

High temperature behaviors of the directed polymer on a cylinder

  title={High temperature behaviors of the directed polymer on a cylinder},
  author={Yu Gu and Tomasz Komorowski},
  • Yu Gu, T. Komorowski
  • Published 14 October 2021
  • Mathematics, Physics
In this paper, we study the free energy of directed polymers on a cylinder of radius L with the inverse temperature β. Assuming the random environment is given by a Gaussian process that is white in time and smooth in space, with an arbitrary compactly supported spatial covariance function, we obtain precise scaling behaviors of the limiting free energy for high temperatures β ≪ 1, followed by large L ≫ 1, in all dimensions. Our approach is based on a perturbative expansion of the PDE hierarchy… 
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