Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation

@article{Bakhtin2018ThermodynamicLF,
  title={Thermodynamic Limit for Directed Polymers and Stationary Solutions of the Burgers Equation},
  author={Yuri Bakhtin and Liying Li},
  journal={Communications on Pure and Applied Mathematics},
  year={2018},
  volume={72}
}
The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and space‐continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the infinite‐volume limit for every fixed asymptotic slope, concentration inequalities for free energy implying a bound on its fluctuation exponent, and straightness estimates implying a bound on the transversal fluctuation exponent. The culmination of this… 
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