Non-existence of bi-infinite polymers
Non-existence of bi-infinite polymers
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DOI：
10.1214/21-ejp731
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发表时间：
2022-01
影响因子：
1.4
通讯作者：
Ofer Busani;T. Seppäläinen
中科院分区：
文献类型：
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作者：
Ofer Busani;T. Seppäläinen
我们发现，非平凡的双无限聚合物吉布斯措施不存在于典型的环境中的反伽马（或对数伽马）定向聚合物模型的平面正方形晶格。精确的技术结果是，除了直线路径上支持的措施，这样的吉布斯措施不存在于几乎每一个环境时，权重是独立和同分布的inversegamma随机变量。证明过程表明，当两个端点的点对点聚合物分布被带到无穷大的相反方向，但不平行于晶格方向，聚合物路径的中点逃逸。证明是基于耦合，平面比较参数，和最近发现的联合分布的Busemann函数。
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 inversegamma 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.