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

摘要

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