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@article{1361781, author = {Lánský, Petr and Polito, Federico and Sacerdote, Laura}, article_number = {3}, doi = {http://dx.doi.org/10.1007/s10955-016-1630-9}, keywords = {FRACTIONAL POISSON-PROCESS; ORDER STATISTIC PROPERTY; POINT-PROCESSES; GROWING NETWORKS; BIRTH PROCESSES}, language = {eng}, issn = {0022-4715}, journal = {JOURNAL OF STATISTICAL PHYSICS}, title = {Generalized Nonlinear Yule Models}, volume = {165}, year = {2016} }
TY - JOUR ID - 1361781 AU - Lánský, Petr - Polito, Federico - Sacerdote, Laura PY - 2016 TI - Generalized Nonlinear Yule Models JF - JOURNAL OF STATISTICAL PHYSICS VL - 165 IS - 3 SP - 661-679 EP - 661-679 SN - 00224715 KW - FRACTIONAL POISSON-PROCESS KW - ORDER STATISTIC PROPERTY KW - POINT-PROCESSES KW - GROWING NETWORKS KW - BIRTH PROCESSES N2 - 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 recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth. ER -
LÁNSKÝ, Petr, Federico POLITO a Laura SACERDOTE. Generalized Nonlinear Yule Models. \textit{JOURNAL OF STATISTICAL PHYSICS}. 2016, roč.~165, č.~3, s.~661-679. ISSN~0022-4715. Dostupné z: https://dx.doi.org/10.1007/s10955-016-1630-9.
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