Memory processes in systems with Zipf-Pareto

JUAN I. PEROTTI; ANA L. SCHAIGORODSKY; BILLONI, ORLANDO V.; ALMEIRA, NAHUEL

Ciudad Autónoma de Buenos Aires, Argentina.

Conferencia; StatPhys-27 (2019); 2019

In this work, using a variant of the Yule-Simon preferential growth model, introduced by Cattuto et al., we provide an explanation of the simultaneous emergence of Zipf?s law and memory effects in the form oflong-range correlations in a chess database. We find that Cattuto?s model is able to reproduce both phenomena, Zipf?s law and the long-range correlations, including the size effects displayed by the Hurst exponent of the corresponding time series. Furthermore, we find burstiness in the activity of the most active players, although the aggregated activity of all players in the database presents an interevent time distribution without burstiness. Since Cattuto?s model is not able to generate times series with a bursty behavior, we made a modification to the memory kernel that allows a bursty dynamics. By introducing a finite memory kernel, we keep the power-law behavior in the popularity distribution and, at the same time, we obtain time series that present burstiness as a consequence of a phase transition in which, at the critical point, the dynamic is ruled by fluctuations.