Exponential Chebyshev Inequalities for Random Graphons and Their Applications

Сибирский математический журнал

article

A. V. Logachov¹  A. A. Mogulskii¹ 

[1] Sobolev Institute of Mathematics;Novosibirsk State University;Novosibirsk State University of Economics and Management;Siberian State University of Geosystems and Technology

关键词: Erd˝os–R´enyi graph;    graphon;    large deviation principle;    law of large numbers;   

DOI  :  10.1134/S0037446620040114

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We prove some exponential Chebyshev inequality and derive the large deviation principle and the law of large numbers for the graphons constructed from a sequence of Erdős–Rényi random graphs with weights. Also, we obtain a new version of the large deviation principle for the number of triangles included in an Erdős–Rényi graph.

【 授权许可】

CC BY