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| Range-Renewal Processes: SLLNs and Power Laws* |
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Citation： |
Xinxing CHEN,Jiansheng XIE,Jiangang YING.Range-Renewal Processes: SLLNs and Power Laws*[J].Chinese Annals of Mathematics B,2022,43(1):63~78 |
| Page view： 463
Net amount： 576 |
Authors： |
Xinxing CHEN; Jiansheng XIE;Jiangang YING |
Foundation： |
National Natural Science Foundation of China (Nos. 11871162,11771286, 11271255, 11271077, 11001173, 11790273) and the Key Laboratory of Mathematics for Nonlinear Science, Fudan University. |
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| Abstract： |
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¨os’ 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. |
Keywords： |
Range renewal process, Strong law of large numbers, Power law |
Classification： |
60F15, 05C80 |
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