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Paper detail

Zero temperature limit for the Brownian directed polymer among Poissonian disasters

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.

preprint2020arXivOpen access
Ryoki FukushimaStefan Junk
math.PR
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Ryoki FukushimaStefan Junk

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