On the Time to Stationarity of Peer-Driven Adoption and Event-Driven Abandonment of Digital Asset Trends on Social Networks

This study explores the intricate dynamics of digital asset engagement, employing a Markov chain model to examine peer-influenced adoption (θ) and event-triggered abandonment (γ) across diverse network structures. The study gives hindsight into mixing time (time to stationarity) analysis, which represents the duration required to achieve a stationary distribution, and investigates its upper bound along with a revised linear programming proof. Simulations reveal the significant impact of network architecture on the spread of adoption and abandonment behaviors over time. Random networks typically demonstrate faster mixing, facilitating rapid information dissemination and market stabilization. In contrast, structured networks like small-world and scale-free exhibit more complex and often slower mixing patterns, showing distinct vulnerabilities or resilience based on the prevailing dynamic. Phase diagrams outline areas of sustainable adoption, critical decline, and swift abandonment, showcasing the long-term viability of various digital asset categories (such as Bitcoin-like, Meme coin-like, and NFT-like) within these network landscapes. The research underscores the crucial influence of network structure on market efficiency, information flow, and the enduring sustainability of digital assets. Additionally, this study aims to provide practical insights for Web3 project teams striving to cultivate sustainable asset ecosystems.