Zero temperature limit for directed polymers and inviscid limit for stationary solutions of stochastic Burgers equation

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.

37 pages, This is an extension of the ergodic program for the Burgers equation in arXiv:1205.6721, arXiv:1406.5660, arXiv:1607.04864

References in corpus (1)

• Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations

Cited by in corpus (5)

• Stationary solutions to the stochastic Burgers equation on the line
• Jointly invariant measures for the Kardar-Parisi-Zhang Equation
• Invariant measures for stochastic conservation laws on the line
• Dynamic polymers: invariant measures and ordering by noise
• Zero temperature limit for the Brownian directed polymer among Poissonian disasters