Gaussian fluctuations of replica overlap in directed polymers

  title={Gaussian fluctuations of replica overlap in directed polymers},
  author={Yu Gu and Tomasz Komorowski},
  journal={Electronic Communications in Probability},
  • Yu Gu, T. Komorowski
  • Published 1 January 2022
  • Mathematics
  • Electronic Communications in Probability
. In this short note, we prove a central limit theorem for a type of replica overlap of the Brownian directed polymer in a Gaussian random environment, in the low temperature regime and in all dimensions. The proof relies on a superconcentration result for the KPZ equation driven by a spatially mollified noise, which is inspired by the recent work of Chatterjee [14]. 




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