Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers Equation

Yuri Bakhtin, Liying Li

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)1358-1397
Number of pages40
JournalJournal of Statistical Physics
Volume172
Issue number5
DOIs
StatePublished - 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

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