混合随机图过程度序列的相变
Phase Transition on The Degree Sequence of a Mixed Random Graph Process
摘要：
研究了连续组合{ \it classical}模型和BA模型的混合随机图过程的度序列问题。请注意，混合模型的步长添加边的数量是随机的，并且是非一致有界的。通过比较论证，揭示了混合模型度分布的相变：{ \it pure}经典模型具有{ \it指数}度序列，而{ \it pure} BA模型和混合模型具有{ \it幂律}度序列.作为该方法的一个应用，还研究了具有{\it硬拷贝}的{\it another}混合模型的度序列的相变，特别是在幂律区域，逆幂可以取大于1的任意值.
英文摘要：
This paper focuses on the problem of the degree sequence for a mixed random graph process which continuously combines the {\it classical} model and the BA model. Note that the number of step added edges for the mixed model is random and non-uniformly bounded. By developing a comparing argument, phase transition on the degree distributions of the mixed model is revealed: while the {\it pure} classical model possesses a {\it exponential} degree sequence, the {\it pure} BA model and the mixed model possess {\it power law} degree sequences. As an application of the methodology, phase transition on the degree sequence of {\it another} mixed model with {\it hard copying} is also studied, especially, in the power law region, the inverse power can take any value greater than 1.
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