Annals of Applied Probability

Zero temperature limit for the Brownian directed polymer among Poissonian disasters

Ryoki Fukushima and Stefan Junk

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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.

Article information

Ann. Appl. Probab., Volume 29, Number 6 (2019), 3821-3860.

Received: October 2018
First available in Project Euclid: 7 January 2020

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82A51 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Directed polymer random environment zero temperature


Fukushima, Ryoki; Junk, Stefan. Zero temperature limit for the Brownian directed polymer among Poissonian disasters. Ann. Appl. Probab. 29 (2019), no. 6, 3821--3860. doi:10.1214/19-AAP1493.

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