A functional central limit theorem for a random ledger model

Distributed ledgers – decentralized databases maintained by network consensus – are often modeled as directed acyclic graphs (DAGs) to capture the causal structure of data addition. Although blockchain systems like Bitcoin use linear chains, alternatives such as tangle in IOTA employ random DAGs. In such mechanisms each new transaction approves multiple predecessors selected through a randomized process. Prior work has established a fluid-limit approximation of the tangle’s growth, governed by a delay differential equation. In this paper we go beyond the fluid limit by analyzing the next-order behavior. We show that the fluctuations around the deterministic limit converge to a Gaussian process and derive a stochastic delay differential equation (SDDE) that describes this next-order approximation.