Mathematical Physics and Probability Reading Seminar

Organisers: Roger Tribe and Oleg Zaboronski

The seminar is dedicated to reading papers relevant to our research (first hour) and discussing research problems with our students (second hour). Everyone is welcome to join in for the whole duration or part of the seminar.

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Term 1. Tuesdays, 1200-1400, B1.12

Topic: Introduction to the Polchinski equation for interacting particle systems

01/10/24. Organisational meeting

08/10/24, 15/10/24. Roger Tribe, Background on stochastic dynamics (Chapter 2 of [1])

22/10/24, 29/10/24. Oleg Zaboronski, Gaussian integration and the Polchinski equation (Sections 3.1, 3.2 of [1]) Notes 1 

05/11/24, 12/11/24, 26/11/24. Oleg Zaboronski, Multi-scale Bakry-Emery criterion (Sections 3.3, 3.5, 6.2, A.2 of [1]) Notes 2

Literature.

[1] Bauerschmidt, R., Bodineau, T. and Dagallier, B., 2023. Stochastic dynamics and the Polchinski equation: an introduction.

arXiv preprint arXiv:2307.07619.

[2] Duch, P., 2024. Construction of Gross-Neveu model using Polchinski flow equation.

arXiv preprint arXiv:2403.18562.

Extra references

[3] On entropy factorisation for weakly-dependent random variables (By Filippo Cesi)

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Term 2. Tuesdays, 1200-1400, B3.01 (Week 1), B1.12 (Weeks 2-10)

Meetings with PhD students

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Term 3. Tuesdays, 1200-1400, B3.01

Topic: Perturbative renormalisation and the Polchinski equation

Literature.

[1] Volkhard F. Muller, 2009.Perturbative Renormalisation by Flow Equations

https://arxiv.org/abs/hep-th/0208211

[2] M. Salmhofer, Renormalisation: An introduction (Springer TMP series)

[3] Duch, P., 2024. Construction of Gross-Neveu model using Polchinski flow equation.

arXiv preprint arXiv:2403.18562.

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