Blockchain and general purpose distributed ledgers are foundational technologies which bring significant innovation in the infrastructures and other underpinnings of our socio-economic systems. These P2P technologies are able to securely diffuse information within and across networks, without need for trustees or central authorities to enforce consensus. In this contribution, we propose a minimalistic stochastic model to understand the dynamics of blockchain-based consensus. By leveraging on random-walk theory, we model block propagation delay on different network topologies and provide a classification of blockchain systems in terms of two emergent properties. Firstly, we identify two performing regimes: a functional regime corresponding to an optimal system function; and a non-functional regime characterised by a congested or branched state of sub-optimal blockchains. Secondly, we discover a phase transition during the emergence of consensus and numerically investigate the corresponding critical point. Our results provide important insights into the consensus mechanism and sub-optimal states in decentralised systems.

中文翻译：

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区块链共识的随机建模

区块链和通用分布式账本是基础技术，为我们社会经济系统的基础设施和其他基础带来重大创新。这些 P2P 技术能够在网络内部和网络之间安全地传播信息，而无需受托人或中央机构来强制达成共识。在这个贡献中，我们提出了一个简约的随机模型来理解基于区块链的共识的动态。通过利用随机游走理论，我们对不同网络拓扑上的块传播延迟进行建模，并根据两个紧急属性对区块链系统进行分类。首先，我们确定了两种执行机制：对应于最优系统功能的功能机制；以及以次优区块链的拥塞或分支状态为特征的非功能性机制。其次，我们发现了共识出现期间的相变，并数值研究了相应的临界点。我们的结果为去中心化系统中的共识机制和次优状态提供了重要的见解。