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On the circle, GMC = CBE

[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1 August 23, 2021 - August 27, 2021

August 24, 2021 (12:00 PM PDT - 01:00 PM PDT)
Speaker(s): Reda Chhaibi (Université de Toulouse III (Paul Sabatier))
Location: MSRI: Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

On The Circle, GMC = CBE


In this talk, I would like to advertise the strict equality between two objects from very different areas of mathematical physics:
- Kahane's Gaussian Multiplicative Chaos (GMC), which uses a log-correlated field as input and plays an important role in certain conformal field theories
- A reference model in random matrices called the Circular Beta Ensemble (CBE)
The goal is to give a precise theorem whose loose form is GMC = CBE. Although it was known that random matrices exhibit log-correlated features, such an exact correspondence is quite a surprise. 

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On The Circle, GMC = CBE

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