On the Limiting Distribution of Shares in Proof-of-Stake

Abstract

Proof-of-Stake (PoS) is often promised to decentralize the blockchain security over Proof-of-Work (PoW) by allowing more people to join without specialized mining hardware. However, there is no consensus in the literature on PoS's centralization, with strong arguments from both sides. Furthermore, theoretical models of PoS often assume very strong conditions that cannot be justified in practice. I relax these assumptions and derive a more realistic model that takes into account trading activity and fees. My model shows that the limiting distribution can be centralized regardless of the initial distribution, reconciling conclusions in prior studies.