Power Law Distributions

Universal Patterns in the Blockchain: Analysis of EOAs and Smart Contracts in ERC20 Token Networks ArXiv ID: 2508.04671 “View on arXiv” Authors: Kundan Mukhia, SR Luwang, Md. Nurujjaman, Tanujit Chakraborty, Suman Saha, Chittaranjan Hens Abstract Scaling laws offer a powerful lens to understand complex transactional behaviors in decentralized systems. This study reveals distinctive statistical signatures in the transactional dynamics of ERC20 tokens on the Ethereum blockchain by examining over 44 million token transfers between July 2017 and March 2018 (9-month period). Transactions are categorized into four types: EOA–EOA, EOA–SC, SC-EOA, and SC-SC based on whether the interacting addresses are Externally Owned Accounts (EOAs) or Smart Contracts (SCs), and analyzed across three equal periods (each of 3 months). To identify universal statistical patterns, we investigate the presence of two canonical scaling laws: power law distributions and temporal Taylor’s law (TL). EOA-driven transactions exhibit consistent statistical behavior, including a near-linear relationship between trade volume and unique partners with stable power law exponents ($γ\approx 2.3$), and adherence to TL with scaling coefficients ($β\approx 2.3$). In contrast, interactions involving SCs, especially SC-SC, exhibit sublinear scaling, unstable power-law exponents, and significantly fluctuating Taylor coefficients (variation in $β$ to be $Δβ= 0.51$). Moreover, SC-driven activity displays heavier-tailed distributions ($γ< 2$), indicating bursty and algorithm-driven activity. These findings reveal the characteristic differences between human-controlled and automated transaction behaviors in blockchain ecosystems. By uncovering universal scaling behaviors through the integration of complex systems theory and blockchain data analytics, this work provides a principled framework for understanding the underlying mechanisms of decentralized financial systems. ...

Discrete $q$-exponential limit order cancellation time distribution ArXiv ID: 2306.00093 “View on arXiv” Authors: Unknown Abstract Modeling financial markets based on empirical data poses challenges in selecting the most appropriate models. Despite the abundance of empirical data available, researchers often face difficulties in identifying the best-fitting model. Long-range memory and self-similarity estimators, commonly used for this purpose, can yield inconsistent parameter values, as they are tailored to specific time series models. In our previous work, we explored order disbalance time series from the broader perspective of fractional L’{“e”}vy stable motion, revealing a stable anti-correlation in the financial market order flow. However, a more detailed analysis of empirical data indicates the need for a more specific order flow model that incorporates the power-law distribution of limit order cancellation times. When considering a series in event time, the limit order cancellation times follow a discrete probability mass function derived from the Tsallis q-exponential distribution. The combination of power-law distributions for limit order volumes and cancellation times introduces a novel approach to modeling order disbalance in the financial markets. Moreover, this proposed model has the potential to serve as an example for modeling opinion dynamics in social systems. By tailoring the model to incorporate the unique statistical properties of financial market data, we can improve the accuracy of our predictions and gain deeper insights into the dynamics of these complex systems. ...