Monotonicity of the Heat Kernel on Graphs  

图上热核的单调性

作　　者：LI Zhan 李展(中国人民大学数学学院,北京100872;郑州大学数学与统计学院,河南郑州450052)

机构地区：[1]School of Mathematics,Renmin University of China,Beijing,100872,P.R.China [2]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,Henan,450052,P.R.China

出　　处：《数学进展》2024年第6期1227-1238,共12页Advances in Mathematics（China）

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)。

摘　　要：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.本文得到了圈上的热核公式的显式表达式,并且作为推论建立了热核的单调性.众所周知,热核可以看作图上的随机游走的转移概率.本文还给出了图上的简单惰性随机游走的概念,得到了无穷道路和圈上的简单惰性随机游走的转移概率.

关 键 词：heat kernel discrete Laplace equation transition probability simple lazy random walk 

分 类 号：O157.5[理学—数学] O175.1[理学—基础数学] O211.62