ZERO TEMPERATURE LIMIT FOR THE BROWNIAN DIRECTED POLYMER AMONG POISSONIAN DISASTERS

• 成果类型: Article
• 署名作者: Fukushima, Ryoki; Junk, Stefan
• 署名单位: Kyoto University; Technical University of Munich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1493
• 发表日期: 2019
• 页码: 3821-3860
• 关键词: stationary solutions

摘要

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.