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Zero temperature limit for the Brownian directed polymer among Poissonian disasters. (English) Zbl 1432.60095
Summary: 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.

MSC:
60K37 Processes in random environments
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
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