Too many frogs cannot fall sleep | Vidéo | Carmin.tv

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Too many frogs cannot fall sleep

By Alexandre Gaudillière

Appears in collection : Analysis and simulations of metastable systems / Analyse et simulation de systèmes métastables

We prove the existence of an active phase for activated random walks on the lattice in all dimensions. This interacting particle system is made of two kinds of random walkers, or frogs: active and sleeping frogs. Active frogs perform simple random walks, wake up all sleeping frogs on their trajectory and fall asleep at constant rate $\lambda$. Sleeping frogs stay where they are up to activation, when waken up by an active frog. At a large enough density, which is increasing in $\lambda$ but always less than one, such frogs on the torus form a metastable system. We prove that $n$ active frogs in a cramped torus will typically need an exponentially long time to collectively fall asleep —exponentially long in $n$. This completes the proof of existence of a non-trivial phase transition for this model designed for the study of self-organized criticality. This is a joint work with Amine Asselah and Nicolas Forien.

Information about the video

Date of recording 04/04/2023
Date of publication 14/04/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.20028103
Cite this video Gaudillière, Alexandre (04/04/2023). Too many frogs cannot fall sleep. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20028103
URL https://dx.doi.org/10.24350/CIRM.V.20028103

Domain(s)

Probability

Bibliography

FORIEN, Nicolas et GAUDILLIÈRE, Alexandre. Active Phase for Activated Random Walks on the Lattice in all Dimensions. arXiv preprint arXiv:2203.02476, 2022. - https://doi.org/10.48550/arXiv.2203.02476
ASSELAH, Amine, FORIEN, Nicolas, et GAUDILLIÈRE, Alexandre. The critical density for activated random walks is always less than 1. arXiv preprint arXiv:2210.04779, 2022. - https://doi.org/10.48550/arXiv.2210.04779

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