A note on comparison theorems for graphs

被引：2
|
作者：
Adriani, Andrea [1 ]
机构：
[1] Univ Insubria, DiSTA, Via Valleggio 11, I-22100 Como, Italy
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 503卷 / 01期
关键词：
Infinite graphs; Comparison theorems; Stochastic properties; FELLER PROPERTY; RICCI CURVATURE; STOCHASTIC COMPLETENESS;
D O I：
10.1016/j.jmaa.2021.125307
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present note we are concerned with the study of curvature-based comparison theorems on graphs related to main stochastic properties, such as the Feller property and stochastic completeness. We show that, under our main hypothesis, whilst previous results concerning stochastic properties are improved, it is not possible to obtain comparison theorems concerning volume growth. Finally, we prove an analogue of the Bishop-Gromov's relative volume comparison theorem and present a series of examples related to various possible notions of curvature. (c) 2021 Elsevier Inc. All rights reserved.
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页数：12
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