On the partition function of a directed polymer in a Gaussian random environment

• 成果类型: Article
• 署名作者: Carmona, P; Hu, Y
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400200213
• 发表日期: 2002
• 页码: 431-457
• 关键词: sherrington-kirkpatrick model; random-walks; fluctuations; time

摘要

The purpose of this work is the study of the partition function Z(n) (beta) of a (d + 1)-dimensional lattice directed polymer in a Gaussian random environment (beta > 0 being the inverse of temperature). In the low-dimensional cases (d = 1 or d = 2), we prove that for all beta > 0, the renormalized partition function Z(n) (beta)/EZ(n) (beta) converges to 0 and the,))() of two independent configurations does not converge to 0. In the correlation ((n)) high dimensional case (d > 3), a lower tail of Z(n) (beta) has been obtained for small beta > 0. Furthermore, we express some thermodynamic quantities in terms of the path measure alone.