证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths...证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths,Ann.Probab.,39(3):1122-1136]中提出的猜想:顶点可迁图上暂留简单随机游走几乎处处有无穷多个切割点.展开更多
In this paper,we prove an explicit formula of the heat kernel on the circle.As a consequence,we establish the monotonicity of the heat kernel.It is well known that the heat kernel can be viewed as the transition proba...In this paper,we prove an explicit formula of the heat kernel on the circle.As a consequence,we establish the monotonicity of the heat kernel.It is well known that the heat kernel can be viewed as the transition probability of random walk on graphs.We also give the definition of the simple lazy random walk on graphs.The transition probabilities of simple lazy random walk on Z and cycle are derived.展开更多
文摘证明了体积增长不低于5次多项式的拟顶点可迁图上的简单随机游走几乎处处有无穷多个切割时,从而有无穷多个切割点.该结论在所论情形下肯定了Benjamini,Gurel-Gurevich和Schramm在文[2011,Cutpoints and resistance of random walk paths,Ann.Probab.,39(3):1122-1136]中提出的猜想:顶点可迁图上暂留简单随机游走几乎处处有无穷多个切割点.
基金Supported by NSFC (Nos.10671182,12061020)NSF of Guizhou Province (Nos.QKH[2019]1123,QKHKY[2021]088,QKHKY[2022]301,QKH-ZK[2021]331)Ph.D. Project of Guizhou Education University (No.2021BS005)。
文摘In this paper,we prove an explicit formula of the heat kernel on the circle.As a consequence,we establish the monotonicity of the heat kernel.It is well known that the heat kernel can be viewed as the transition probability of random walk on graphs.We also give the definition of the simple lazy random walk on graphs.The transition probabilities of simple lazy random walk on Z and cycle are derived.
