Dr Jessica Jay
Lecturer in Security and Protection ScienceResearch Interests
My main area of research is Probability, in particular Interacting Particle Systems (IPS's). These are certain continuous time Markov processes on discrete state spaces with many applications, for example traffic/data flow, voting/opinion dynamics and also tumour growth.
Currently, I am interested in exploring links between IPS's and other areas of Pure Mathematics such as Combinatorics and Algebra. For example, comparing stationary measures for certain equivalent particle systems often leads to purely probabilistic proofs of both classic and new q-series identitites of combinatorial significiance (e.g. the Jacobi triple product identitiy).
I am also interested in applications of IPS's in the real world. If this is something you have ideas about then please feel free to get in touch!
Career Details
I was awarded my PhD in Mathematics from the Univeristy of Bristol in February 2023, under the supervision of Prof. Márton Balázs. From October 2022 until August 2024, I was a Heilbronn Research Fellow at the University of Bristol.
Web Links
Current Teaching
- MATH 332/432: Stochastic Processes
PhD Supervision Interests
I am interested in supervising PhD students who have a strong interest and background in discrete probability. My current research is in the theory of interacting particle systems. One potential project is to study the second class particle behaviour of certain reversible interacting particle systems. Interacting particle systems have been shown to have strong links to other areas of mathematics such as combinatorics (via partitions) and algebra (some systems can be constructed from certain quantum groups). I would be happy to discuss the potential for interested students to work on a jointly supervised project studying these links further. If you would like to know more, please feel free to get in touch!
Stochastics and Influences
Invited talk
University of Bristol Probability Seminar
Invited talk
Probability, Analysis and Dynamics 2025
Participation in conference - Academic
Royal Institution Mathematics Masterclass
Invited talk
Advances in Combinatorial and Algebraic Probability
Participation in workshop, seminar, course
- Combinatorics
- Probability