## Annals of Applied Probability

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

### Zero temperature limit for the Brownian directed polymer among Poissonian disasters

Ryoki Fukushima and Stefan Junk

#### 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.

#### Article information

**Source**

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

**Dates**

Received: October 2018

First available in Project Euclid: 7 January 2020

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1578366327

**Digital Object Identifier**

doi:10.1214/19-AAP1493

**Mathematical Reviews number (MathSciNet)**

MR4047993

**Zentralblatt MATH identifier**

07172347

**Subjects**

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)

**Keywords**

Directed polymer random environment zero temperature

#### Citation

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. https://projecteuclid.org/euclid.aoap/1578366327