Zero temperature limit for the Brownian directed polymer among Poissonian disasters

Ryoki Fukushima; Stefan Junk

doi:10.1214/19-AAP1493

Zero temperature limit for the Brownian directed polymer among Poissonian disasters

Ryoki Fukushima, Stefan Junk

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3821-3860
Number of pages	40
Journal	Annals of Applied Probability
Volume	29
Issue number	6
DOIs	https://doi.org/10.1214/19-AAP1493
Publication status	Published - 2019
Externally published	Yes

Keywords

Directed polymer
Random environment
Zero temperature

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/19-AAP1493

Cite this

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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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AU - Junk, Stefan

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N2 - 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.

AB - 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.

KW - Directed polymer

KW - Random environment

KW - Zero temperature

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Zero temperature limit for the Brownian directed polymer among Poissonian disasters

Abstract

Keywords

ASJC Scopus subject areas

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