Weakly pinned random walk on the wall: pathwise descriptions of the phase transition
Weakly pinned random walk on the wall: pathwise descriptions of the phase transition
复制标题
墙上的弱固定随机游走：相变的路径描述
DOI：
10.1016/s0304-4149(01)00118-1
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发表时间：
2001
影响因子：
1.4
通讯作者：
N. Yoshida
中科院分区：
文献类型：
--
作者：
Y. Isozaki;N. Yoshida
我们考虑一个一维的随机游动，条件是保持非负的，是“弱钉扎”为零。这个模型是已知的表现出相变的弱钉扎的强度变化。我们证明路径空间极限定理描述的宏观形状的路径的所有值的钉扎强度。如果小于（或小于），等于）的临界强度，则极限过程是布朗曲流（分别）。反射布朗运动）。如果钉扎强度是超临界的，则极限过程是一个正常返的马尔可夫链，具有强混合性质。
We consider a one-dimensional random walk which is conditioned to stay non-negative and is “weakly pinned” to zero. This model is known to exhibit a phase transition as the strength of the weak pinning varies. We prove path space limit theorems which describe the macroscopic shape of the path for all values of the pinning strength. If the pinning is less than (resp. equal to) the critical strength, then the limit process is the Brownian meander (resp. reflecting Brownian motion). If the pinning strength is supercritical, then the limit process is a positively recurrent Markov chain with a strong mixing property.