View on GitHub


Blockchain stochastics: Stochastic models for blockchain systems analysis

You will find on this page the research publications associated to the BLOCKASTICS project as well as some graduate level course materials.


A blockchain is a distributed ledger maintained by achieving consensus among a number of nodes in a peer-to-peer network. The blockchain technology has attracted a lot of interest after the advent of the bitcoin cryptocurrency in 2008. Since then, the blockchain concept has been used to develop decentralized systems to store and maintain the integrity of time-stamped transaction data across peer-to-peer networks. Besides the creation of a digital currency, blockchain applications include the sharing of IT resources, the registration of authentication certificate or the implementation of smart contracts.


The BLOCKASTICS project aims at building mathematical models to analyse the consensus protocols that allow the nodes to agree on a common data history. The consensus protocol must be analysed through three dimensions:

  1. Efficiency, characterized by the amount of data being processed per time unit.

  2. Decentralization, measured by the fairness of the decision-making power distribution between network actors.

  3. Security, assessed by the probability of success of attacks on the blockchain.


Course materials

Advanced Topics in Applied Probability at UC, Santa Barbara

I taught a graduate class during spring quarter 2022 (ten weeks) in the PSTAT department at UC, Santa Barbara. Here are the lecture notes.

(Please note that it is a work in progress, I am planning to write a more comprehensive overview with additional references)

BFS summer school

The material of this section is made of 3 45-50 minutes lectures covered during the first Bachelier Finance Society summer school that took place in September 2021.

Section Material
Blockchain concepts Slides, Recording
Simple models for blockchain performance analysis Slides, Recording
Risk models and blockchain mining Slides, Recording

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.