Research On Power Law Phenomena And Selection Behaviors

Various phenomena governed by power law distributions are ubiquitous in nature and society, thus their study carries broad and far-reaching significance. There are lots of power law phenomena resulted by human's selective behaviors in network, which is a focus of recent research in the physical, mathematical and sociological fields.This dissertation analyzed the human's selective behaviors and pointed out these behaviors are rational and self-interested. On the basis of this, it established a model by selective trial and got a generation method for power law distribution. It demonstrated that the power law could be explained reasonably by probability theory.Moreover, this dissertation extended the probability trials and models for power-law phenomena with different index numbers, and presented a general selective model. It also discovered the close relationship between power law and index law. This dissertation supplied the power-law generation means and supported reduction method, which meant that simple and independent human behaviors lead power law to be ubiquitous.Based on this model, the discrete preferential transformation was presented with its continuous counterpart by discerption method and fix-threshold distribution. It put forward to two comparison functions which associated the discrete distribution and continuous ones. It also extended the traditional probability theory.Meanwhile, the preferential tree and graph were presented and analyzed. This was basical reasearch for the graph in which the connections of vertexes was guided by the preference index. And it put forward a new method called preferential chain method for generating power-law graph and index-law graph.This dissertation consists of 5 chapters, including 36 figures, 7 tables, 98 formulas and 100 references.