publication . Preprint . Other literature type . Article . 2016

Generalized Nonlinear Yule Models

Petr Lansky; Federico Polito; Laura Sacerdote;
Open Access English
  • Published: 04 Oct 2016
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random ...
free text keywords: Mathematics - Probability, 60G22, 60J80, 05C80, Mathematical Physics, Statistical and Nonlinear Physics, Random graph, Mean value, Mathematics, Fractional calculus, Calculus, Asymptotic analysis, Nonlinear system, Macroevolution, Applied mathematics, Point process, Fractional Poisson process
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