论文标题
双涉及聚合物Gibbs措施的不存在
Non-existence of bi-infinite polymer Gibbs measures
论文作者
论文摘要
我们表明，在平面正方形晶格上的典型环境（或log-gamma）定向聚合物模型的典型环境中，非平凡的双限制聚合物Gibbs测量不存在。确切的技术结果是，除了直线路径上支持的措施外，当权重独立并且分布相同的逆伽马随机变量时，几乎每个环境中都不存在此类Gibbs度量。证明是通过表明当点对点聚合物分布的两个端点以相反的方向将无穷大的端点带到无穷大时，而不是平行于晶格方向时，聚合物路径的中点逸出。证明是基于耦合，平面比较论点以及最近发现的Busemann函数的联合分布的。
We show that nontrivial bi-infinite polymer Gibbs measures do not exist in typical environments in the inverse-gamma (or log-gamma) directed polymer model on the planar square lattice. The precise technical result is that, except for measures supported on straight-line paths, such Gibbs measures do not exist in almost every environment when the weights are independent and identically distributed inverse-gamma random variables. The proof proceeds by showing that when two endpoints of a point-to-point polymer distribution are taken to infinity in opposite directions but not parallel to lattice directions, the midpoint of the polymer path escapes. The proof is based on couplings, planar comparison arguments, and a recently discovered joint distribution of Busemann functions.
