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December 2019 Zero temperature limit for the Brownian directed polymer among Poissonian disasters
Ryoki Fukushima, Stefan Junk
Ann. Appl. Probab. 29(6): 3821-3860 (December 2019). DOI: 10.1214/19-AAP1493

Abstract

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.

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Ryoki Fukushima. Stefan Junk. "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

Information

Received: 1 October 2018; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172347
MathSciNet: MR4047993
Digital Object Identifier: 10.1214/19-AAP1493

Subjects:
Primary: 60K37
Secondary: 60K35, 82A51, 82D30

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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