Asymptotic behavior of the transition probability of a random walk on an infinite graph
Asymptotic behavior of the transition probability of a random walk on an infinite graph
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无限图上随机游走的转移概率的渐近行为
DOI：
10.1006/jfan.1998.3322
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发表时间：
1998
影响因子：
1.7
通讯作者：
T. Sunada
中科院分区：
文献类型：
--
作者：
M. Kotani;T. Shirai;T. Sunada
利用谱几何的思想，得到了满足一定周期条件的无限图上可逆随机游动的一个渐近性质。在讨论过程中，我们利用微扰理论求出了扭转移算子的最大本征值。结果，建立了一个粒子从x到达y的概率p（n，x，y）在时间n到达无穷大的渐近式.
Ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a reversible random walk on an infinite graph satisfying a certain periodic condition. In the course of our argument, we employ perturbation theory for the maximal eigenvalues of twisted transition operator. As a result, an asymptotic of the probabilityp(n, x, y) that a particle starting atxreachesyat timenasngoes to infinity is established.