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 show that the free energy exists and is continuous at zero-temperature.
"Zero temperature limit for the Brownian directed polymer among Poissonian disasters." Ann. Appl. Probab. 29 (6) 3821 - 3860, December 2019. https://doi.org/10.1214/19-AAP1493