Interacting particle systems and related fields / Systèmes de particules en interaction et domaines connexes

Collection Interacting particle systems and related fields / Systèmes de particules en interaction et domaines connexes

Organizer(s) Bernardin, Cédric ; Franco, Tertuliano ; Gabrielli, Davide ; Gonçalves, Patricia ; Sethuraman, Sunder ; Simon, Marielle

Date(s) 22/09/2025 - 26/09/2025

linked URL https://conferences.cirm-math.fr/3335.html

00:00:00 / 00:00:00

2 5

Studying the phase transistion(s) for directed polymers in random environment

By Hubert Lacoin

The Directed Polymer in a Random Environment is obtained by weighting the trajectories of finite length simple random walk using an i.i.d. random environment. It is one of the simplest disordered models in statistical mechanics, and one for which the disorder-induced phase transition has been intensively studied. When the intensity of the disorder increases, the systems behavior changes drastically: at high temperature (low disorder intensity) the trajectories of the polymer are diffusive with a behavior which is very similar to that of the simple random walk, at low temperature, the trajectories of the polymer are conjecture to concentrate on a narrow space-time corridor, and its end-point distribution is localized. In this talk we will survey recent results obtained in collaboration with S. Junk concerning the sharpness and smoothness of this transition.

Information about the video

Date of recording 22/09/2025
Date of publication 08/10/2025
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.20390903
Cite this video Lacoin, Hubert (22/09/2025). Studying the phase transistion(s) for directed polymers in random environment . CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20390903
URL https://dx.doi.org/10.24350/CIRM.V.20390903

Domain(s)

Probability

Bibliography

JUNK, Stefan et LACOIN, Hubert. Strong disorder and very strong disorder are equivalent for directed polymers. arXiv preprint arXiv:2402.02562, 2024. - https://doi.org/10.48550/arXiv.2402.02562
JUNK, Stefan et LACOIN, Hubert. The tail distribution of the partition function for directed polymers in the weak disorder phase. Communications in Mathematical Physics, 2025, vol. 406, no 3, p. 48. - https://doi.org/10.1007/s00220-025-05246-0
LACOIN, Hubert. The localization transition for the directed polymer in a random environment is smooth. arXiv preprint arXiv:2505.13382, 2025. - https://doi.org/10.48550/arXiv.2505.13382

MSC codes

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