Number of paths in oriented percolation as zero temperature limit of directed polymer

• 成果类型: Article
• 署名作者: Fukushima, Ryoki; Junk, Stefan
• 署名单位: University of Tsukuba; Tohoku University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01130-3
• 发表日期: 2022
• 页码: 1119-1151
• 关键词: random environment; contact process

摘要

We prove that the free energy of directed polymer in Bernoulli environment converges to the growth rate for the number of open paths in super-critical oriented percolation as the temperature tends to zero. Our proof is based on rate of convergence results which hold uniformly in the temperature. We also prove that the convergence rate is locally uniform in the percolation parameter inside the super-critical phase, which implies that the growth rate depends continuously on the percolation parameter.