The free energy of the random walk pinning model
The free energy of the random walk pinning model
复制标题
随机游走钉扎模型的自由能
DOI：
10.1016/j.spa.2017.04.015
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发表时间：
2018
影响因子：
1.4
通讯作者：
Nakashima Makoto
中科院分区：
文献类型：
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作者：
Fumikazu Nagasato;Masaaki Suzuki and Anh T. Tran;FUMIKAZU NAGASATO AND ANH T. TRAN;長郷 文和，鈴木 心之助;Fumikazu Nagasato and Shinnosuke Suzuki;Fumikazu Nagasato;Shinnosuke Suzuki;長郷 文和;Fumikazu Nagasato;Shinnosuke Suzuki;Fumikazu Nagasato;Shinnosuke Suzuki;Fumikazu Nagasato;Shinnosuke Suzuki;Fumikazu Nagasato;長郷 文和;長郷 文和;Nakashima Makoto
我们考虑随机游动钉扎模型。这是在Zd上的随机游动，它的定律被给出为Gibbs度量μN，Yβ，其中聚合物度量μN，Yβ是通过使用碰撞局部时间与到时间N的另一个简单的对称随机游动Y在Zd上定义的。然后，已知至少两个相变的定义，用配分函数和自由能来描述。在本文中，我们将证明这两个临界点重合，并用变分表示给出自由能的显式公式。证明了当β小于临界点时，μN，Yβ下的X几乎必然满足中心极限定理和不变原理。
We consider the random walk pinning model. This is a random walk on Z d whose law is given as the Gibbs measure μ N, Y β, where the polymer measure μ N, Y β is defined by using the collision local time with another simple symmetric random walk Y on Z d up to time N. Then, at least two definitions of the phase transitions are known, described in terms of the partition function and the free energy. In this paper, we will show that the two critical points coincide and give an explicit formula for the free energy in terms of a variational representation. Also, we will prove that if β is smaller than the critical point, then X under μ N, Y β satisfies the central limit theorem and the invariance principle P Y-almost surely.