学术报告（李泉林 12.3）

This talk provides a comprehensive framework to set up probability theory of blockchain, including stochastic dynamic systems, multi-dimensional pyramid Markov processes, Markov processes of cross competition, multi-dimensional pyramid Markov decision processes, Markov processes on either chains, trees or directed acyclic graphs, and stochastic game of blockchain. We address several interesting and challenging issues or topics related to the multi-dimensional Markov (decision) processes, and further caring for, for example,

(1) Studying the multi-dimensional Markov processes and Markov processes on graphs, establishing the stable conditions, the steady-state probability vector, the first passage time and so forth. Really, these Markov processes of blockchain bring you to enter a queer theoretical space from some new interesting research perspective.

(2) Block reward, transaction fee, and further economics of blockchain greatly motivate many miners to form some selfish mining alliances (or pools) evolutionarily, while the selfish mining pools can lead to various attacks on security and privacy of blockchain. In this situation, we provide a new and unified framework to study the selfish mining pools. the physical structure of blockchain is given a detailed observation and interpretation in terms of the pyramid Markov processes, and the performance measures are set up in detail so that the orphan blocks and the uncle blocks are analyzed quantitatively. This should be regarded as a key advance of blockchain theory.

(3) The multi-dimensional Markov processes and the Markov processes on graphs can be applied to analyzing dynamic control of blockchain and design of consensus mechanisms. We believe that this can motivate a series of promising future research on innovative development of blockchain technologies.