论文标题
通过部分循环搜索程序，基于环路的马尔可夫链的缩放限制在电阻空间上
Scaling limits of loop-erased Markov chains on resistance spaces via a partial loop-erasing procedure
论文作者
论文摘要
我们介绍了部分循环浏览操作员。我们表明，通过将部分循环渗透算子的完善序列应用于有限的马尔可夫链中，我们获得了与按时间顺序排列的马尔可夫链相等的过程。作为一种应用，我们在电阻空间的有界域上构造基于环的随机路径，作为马尔可夫链的弱极限，在近似空间的有限序列上擦除，并且极限与近似序列无关。我们构造的随机路径几乎肯定是简单的路径，并且可以将其视为扩散过程路径的循环。最后，我们表明存在基于环的随机步行的缩放限制在Sierpiński地毯图上存在，并且等同于Sierpińksi地毯上的基于环的随机路径。
We introduce partial loop-erasing operators. We show that by applying a refinement sequence of partial loop-erasing operators to a finite Markov chain, we get a process equivalent to the chronological loop-erased Markov chain. As an application, we construct loop-erased random paths on bounded domains of resistance spaces as the weak limit of the loop erasure of the Markov chains on a sequence of finite sets approximating the space, and the limit is independent of the approximating sequences. The random paths we constructed are simple paths almost surely, and they can be viewed as the loop-erasure of the paths of the diffusion process. Finally, we show that the scaling limit of the loop-erased random walks on the Sierpiński carpet graphs exists, and is equivalent to the loop-erased random paths on the Sierpińksi carpet.
