Fractional stochastic model of citation dynamics with memory and volatility

Area of Science:

• Network theory
• Science of science
• Bibliometrics

Background:

• Citation networks show log-normal distributions but also power-law behavior in high-citation regimes, a contradiction.
• Understanding citation dynamics is crucial for network theory and the science of science.

Purpose of the Study:

• To resolve the apparent contradiction in citation distribution laws.
• To introduce a unified framework for understanding citation dynamics.

Main Methods:

• Developed a stochastic model of latent attention using fractional Brownian motion.
• Analyzed the variance of log citation counts over time.
• Simulated attention dynamics and analyzed arXiv e-prints.

Main Results:

• Identified a power-law relationship between the variance of log citation counts and time since publication (t^H).
• Demonstrated that antipersistent attention (H<1/2) leads to log-normal distributions, while persistent attention (H>1/2) leads to power laws.
• Empirical analysis of arXiv data showed antipersistent attention (H≈0.13).

Conclusions:

• The study provides a unifying framework linking memory effects and attention fluctuations to citation network evolution.
• The findings offer a resolution to the log-normal-power-law contradiction in citation distributions.
• The model advances understanding of collective attention dynamics in science and other fields.