December 2021 CDT in Maths of Random Systems Workshop

Zheneng Xie: Scaling Limits of Random Graphs

The scaling limit of directed random graphs remains relatively unexplored compared to their undirected counterparts. In contrast, many real-world networks, such as links on the world wide web, financial transactions and “follows” on Twitter, are inherently directed. Previous work by Goldschmidt and Stephenson established the scaling limit for the strongly connected components (SCCs) of the Erdős--Rényi model in the critical window when appropriately rescaled. In this talk, we present a result showing the SCCs of another class of critical random directed graphs will converge when rescaled to the same limit. Central to the proof is an exploration of the directed graph and subsequent encodings of the exploration as real valued random processes. We aim to present this exploration algorithm and other key components of the proof.  

Lancelot Da Costa: Adaptive agents: from theory to practice

The scaling limit of directed random graphs remains relatively unexplored compared to their undirected counterparts. In contrast, many real-world networks, such as links on the world wide web, financial transactions and “follows” on Twitter, are inherently directed. Previous work by Goldschmidt and Stephenson established the scaling limit for the strongly connected components (SCCs) of the Erdős -- Rényi model in the critical window when appropriately rescaled. In this talk, we present a result showing the SCCs of another class of critical random directed graphs will converge when rescaled to the same limit. Central to the proof is an exploration of the directed graph and subsequent encodings of the exploration as real valued random processes. We aim to present this exploration algorithm and other key components of the proof.

Professor Terry Lyons: From Mathematics to Data Science and Back

We give an overview of the interaction between rough path theory and data science at the current time.