论文标题
股份证明协议证明 - 集中和相变的稳定性
Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions
论文作者
论文摘要
本文关注的是在加密货币中股票的稳定性，在该加密货币中，根据股份协议的证明，将发行新硬币。我们在各种奖励计划下确定了大型，中小型投资者，并表明这些投资者的限制行为是不同的 - 对于大型投资者而言，他们的股票稳定，而对于中小型投资者而言，其股票可能是波动的甚至缩水到零。例如，有了几何奖励，有混乱的集中化，所有股份最终都会以随机的方式集中于一个投资者。这导致了相变现象，并且表征了稳定性的阈值。为了响应区块链网络中日益增长的活动，我们还提出和分析了POS协议的动态人群模型，这使投资者的数量可以随着时间的推移而增长。提供数值实验来证实我们的理论。
This paper is concerned with the stability of shares in a cryptocurrency where the new coins are issued according to the Proof of Stake protocol. We identify large, medium and small investors under various rewarding schemes, and show that the limiting behaviors of these investors are different -- for large investors their shares are stable, while for medium to small investors their shares may be volatile or even shrink to zero. For instance, with a geometric reward there is chaotic centralization, where all the shares will eventually concentrate on one investor in a random manner. This leads to the phase transition phenomenon, and the thresholds for stability are characterized. In response to the increasing activities in blockchain networks, we also propose and analyze a dynamical population model for the PoS protocol, which allows the number of investors to grow over the time. Numerical experiments are provided to corroborate our theory.
