Download relaxation dynamics on the WWW following newspaper publication of URL

Abstract

A few key properties of the World-Wide-Web (WWW) has been established indicating the lack of any characteristic scales for the WWW, both in its topology and in its dynamics. Here, we report an experiment which quantifies another power law describing the dynamical response of the WWW to a Dirac-like perturbation, specifically how the popularity of a web site evolves and relaxes as a function of time, in response to the publication of a notice/advertisement in a newspaper. Following the publication of an interview of the authors by a journalist which contained our URL, we monitored the rate of downloads of our papers and found it to obey a $1/t^b$ power law with exponent $b=0.58\pm 0.03$. This small exponent implies long-term memory and can be rationalized using the concept of persistence, which specifies how long a relaxing dynamical system remains in a neighborhood of its initial configuration.