Jean Morlet Chair - Geometric and Probabilistic Aspects in Quantum Field Theory / Chaire Jean Morlet Conférence - Aspects géométriques et probabilistes de la théorie quantique des champs

Collection Jean Morlet Chair - Geometric and Probabilistic Aspects in Quantum Field Theory / Chaire Jean Morlet Conférence - Aspects géométriques et probabilistes de la théorie quantique des champs

Organizer(s) Peltola, Eveliina ; Rhodes, Rémi

Date(s) 31/08/2026 - 04/09/2026

linked URL https://conferences.cirm-math.fr/3540.html

00:00:00 / 00:00:00

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FK decorated planar maps: the q=4 phase transition

By Ellen Powell

The critical Fortuin–Kasteleyn random planar map with parameter q > 0 is a model of random (discretised) surfaces decorated by loops, related to the q-state Potts model. For q < 4, Sheffield established a scaling limit result for these discretised surfaces, where the limit is described by a so-called Liouville quantum gravity surface decorated by a conformal loop ensemble. At q = 4 a phase transition occurs, and the correct rescaling needed to obtain a limit has so far remained unclear. I will talk about joint work with William Da Silva, XinJiang Hu, and Mo Dick Wong, where we identify the right rescaling at this critical value and prove a number of convergence results.

Information about the video

Date of recording 31/08/2026
Date of publication 05/10/2026
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20531103
Cite this video Powell, Ellen (31/08/2026). FK decorated planar maps: the q=4 phase transition. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20531103
URL https://dx.doi.org/10.24350/CIRM.V.20531103

Domain(s)

Probability

Bibliography

DA SILVA, William, HU, Xingjian, POWELL, Ellen, et al. Scaling limits of critical FK-decorated random planar maps with $ q= 4$. arXiv preprint arXiv:2511.21480, 2025. - https://doi.org/10.48550/arXiv.2511.21480

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