Zero temperature limit for the Brownian directed polymer among Poissonian disasters

Abstract

We study a continuum model of directed polymer in random environment. The law of the polymer is defined as the Brownian motion conditioned to survive among space-time Poissonian disasters. This model is well-studied in the positive temperature regime. However, at zero-temperature, even the existence of the free energy has not been proved. In this article, we prove that the free energy exists and is continuous at zero-temperature.

40 pages

References in corpus (1)

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

Cited by in corpus (1)

• Number of paths in oriented percolation as zero temperature limit of directed polymer