Stochastic Modeling of Path Length Dynamics in Ethereum’s Merkle Patricia Tries

This study presents a novel probabilistic framework for analyzing path length distributions in Merkle Patricia Tries, the foundational data structure of Ethereum’s state management system. We develop a mathematical model characterizing the probability distribution of path lengths for randomly generated Ethereum addresses and validate it through extensive computational simulations. Our findings reveal the logarithmic growth of average path lengths with respect to the number of addresses, confirming a critical property for Ethereum’s scalability. The study demonstrates remarkable accuracy in predicting average path lengths, with discrepancies between theoretical and empirical results remaining below 0.01 across tested scales from 1000 to 300 million addresses, encompassing Ethereum’s current state size. We identify and confirm the right-skewed nature of path length distributions, providing essential insights into worst-case scenarios and informing optimization strategies. Statistical analysis, including chi-square goodness-of-fit tests, strongly supports the model’s accuracy. This research bridges a significant gap between theoretical computer science and practical blockchain engineering, offering immediate applications for Ethereum client optimization, stateless client development, and informed protocol upgrade decisions.