Generalized Nonlinear Yule Models

LÁNSKÝ, Petr, Federico POLITO and Laura SACERDOTE. Generalized Nonlinear Yule Models. JOURNAL OF STATISTICAL PHYSICS. 2016, vol. 165, No 3, p. 661-679. ISSN 0022-4715. Available from: https://dx.doi.org/10.1007/s10955-016-1630-9.

Basic information

• Original name: Generalized Nonlinear Yule Models
• Name in Czech: Zobecnene nelinearni Yulovy modely
• Authors: LÁNSKÝ, Petr (203 Czech Republic, guarantor, belonging to the institution), Federico POLITO (380 Italy) and Laura SACERDOTE (380 Italy).
• Edition: JOURNAL OF STATISTICAL PHYSICS, 2016, 0022-4715.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 1.349
• RIV identification code: RIV/00216224:14310/16:00088377
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1007/s10955-016-1630-9
• UT WoS: 000386681800008
• Keywords in English: FRACTIONAL POISSON-PROCESS; ORDER STATISTIC PROPERTY; POINT-PROCESSES; GROWING NETWORKS; BIRTH PROCESSES
• Tags: AKR, rivok
• Tags: International impact, Reviewed

Abstract

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.

Links

• GA15-06991S, research and development project: Name: Analýza funkcionálních dat a související témata

Investor: Czech Science Foundation