## Abstract

We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer measures and one-sided infinite minimizers for the associated variational principle, and used these objects for the study of global stationary solutions of the Burgers equation with positive or zero viscosity and random kick forcing, on the entire real line. In this paper, we prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation.

Original language | English (US) |
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Pages (from-to) | 1358-1397 |

Number of pages | 40 |

Journal | Journal of Statistical Physics |

Volume | 172 |

Issue number | 5 |

DOIs | |

State | Published - Sep 1 2018 |

## Keywords

- Directed polymers
- KPZ universality
- One-force-one-solution principle
- Random environment
- Stationary solutions
- Stochastic Burgers equation
- Thermodynamic limit
- Zero-temperature limit
- Zero-viscosity limit

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics