Automated market makers (AMMs) quote prices from pool state rather than from a limit order book. AMM pools often stay close to a reference price because arbitrageurs correct profitable mispricing. A large part of decentralized finance therefore relies on a simple economic premise: once the AMM price drifts away from the reference price, arbitrage incentives push it back. This paper studies when that premise is strong enough to guarantee block-scale stability. We model the gap between the reference price and the AMM price as a stochastic tracking error, treat arbitrage as the corrective input, and place blockchain execution inside the loop through fees, discrete blocks, transaction ordering, delays, and transaction failure. The detailed execution layer is reduced to the total successful correction confirmed in each block. Under a block-level correction condition, we prove geometric ergodicity of the tracking error and obtain explicit one-step bounds that connect tracking quality to liquidity and execution quality. We also show in a constant-product example how fees, fixed execution costs, and local liquidity map into the no-trade band and the optimal corrective trade. Finally, we build empirical proxies for the theorem quantities from realized block data and use them to organize reduced and mechanism-focused simulations whose comparative statics are consistent with the theory. The contribution is to turn a basic economic intuition behind decentralized finance into a quantitative stability statement together with a tractable calibration interface.

翻译：自动化做市商（AMM）根据池内状态而非限价订单簿报价。由于套利者会修正有利可图的错误定价，AMM池的价格通常接近参考价格。因此，去中心化金融的很大一部分依赖于一个简单的经济前提：一旦AMM价格偏离参考价格，套利动机就会将其推回。本文研究了该前提何时足够强大以保证区块尺度的稳定性。我们将参考价格与AMM价格之间的差距建模为随机追踪误差，将套利视为修正输入，并通过费用、离散区块、交易排序、延迟和交易失败将区块链执行纳入分析循环。详细的执行层被简化为每个区块中成功修正的总量。在区块级修正条件下，我们证明了追踪误差的几何遍历性，并得到了连接追踪质量与流动性和执行质量的显式单步界限。我们还在一个恒定乘积示例中展示了费用、固定执行成本和局部流动性如何映射到无交易带和最优修正交易。最后，我们根据实际区块数据构建了定理数量的经验代理，并利用它们组织了简化且聚焦于机制的模拟，其比较静态结果与理论一致。本文的贡献是将去中心化金融背后的基本经济直觉转化为定量稳定性陈述以及一个易处理的校准接口。