INFLUENCE OF SPATIAL CORRELATION FOR DIRECTED POLYMERS

• 成果类型: Article
• 署名作者: Lacoin, Hubert
• 署名单位: Roma Tre University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP553
• 发表日期: 2011
• 页码: 139-175
• 关键词: random environment; superdiffusivity; fluctuations

摘要

In this paper, we study a model of a Brownian polymer in R+ x R-d, introduced by Rovira and Tindel [J. Fund. Anal. 222 (2005) 178-201]. Our investigation focuses mainly on the effect of strong spatial correlation in the environment in that model in terms of free energy, fluctuation exponent and volume exponent. In particular, we prove that under some assumptions, very strong disorder and superdiffusivity hold at all temperatures when d >= 3 and provide a novel approach to Petermann's superdiffusivity result in dimension one [Superdiffusivity of directed polymers in random environment (2000) Ph.D. thesis]. We also derive results for a Brownian model of pinning in a nonrandom potential with power-law decay at infinity.