Range-Renewal Processes:SLLNs and Power Laws

• 作者: Xinxing CHEN Jiansheng XIE Jiangang YING
• 来源期刊: 数学年刊B辑（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 63-78
• 页数: 16页
• 语种: 英文
• DOI: 10.1007/s11401-022-0305-x

摘要

Given n samples (viewed as an n-tuple) of a γ-regular discrete distribution π,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN results (of Dvoretzky-Erd(o)s' type).Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1 + γ They also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distributions with constant exponent 2.This exponent is obviously independent of the parameter γ ∈ (0,1),which is a surprise to us at first sight.