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

Zero temperature limit for the Brownian directed polymer among Poissonian disasters