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Cutoff phenomenon for the asymmetric simple exclusion process
Multi angle
Authors : Labbé, Cyril (Author of the conference)
CIRM (Publisher )
37A25 - Ergodicity, mixing, rates of mixing
60J27 - Continuous-time Markov processes on discrete state spaces
82C22 - Interacting particle systems
CIRM (Publisher )
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Abstract :
I will consider the asymmetric simple exclusion process on a linear lattice of N sites, and I will present a result on the asymptotic (in N) behaviour of the distance to equilibrium of this process starting from the "worst" initial condition. This result shows a cutoff phenomenon: instead of decaying smoothly with time, the distance to equilibrium falls abruptly at some deterministic time. This is a joint work with Hubert Lacoin (IMPA).
Keywords : Cutoff; exclusion process; mixing time; Burgers equation
MSC Codes : Keywords : Cutoff; exclusion process; mixing time; Burgers equation
37A25 - Ergodicity, mixing, rates of mixing
60J27 - Continuous-time Markov processes on discrete state spaces
82C22 - Interacting particle systems
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 04/11/2019 Conference Date : 14/10/2019 Subseries : Research talks arXiv category : Probability ; Mathematical Physics Mathematical Area(s) : PDE ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:52:39 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-14_Labbe.mp4 
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Information on the Event
Event Title : PDE/Probability Interactions: Particle Systems, Hyperbolic Conservation Laws / Interactions EDP/Probabilités : systèmes de particules, lois de conservation hyperboliquesEvent Organizers : Caputo, Pietro ; Fathi, Max ; Guillin, Arnaud ; Reygner, Julien Dates : 14/10/2019 - 18/10/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2083.html
Citation Data
DOI : 10.24350/CIRM.V.19570303Cite this video as: Labbé, Cyril (2019). Cutoff phenomenon for the asymmetric simple exclusion process. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19570303 URI : http://dx.doi.org/10.24350/CIRM.V.19570303 |
See Also
- [Multi angle] Adding small viscosity to hyperbolic (stochastic) conservation laws / Author of the conference Boritchev, Alexandre.
- [Multi angle] Homogenizations for Hamilton-Jacobi PDEs and Hamiltonian ODEs / Author of the conference Rezakhanlou, Fraydoun.
- [Multi angle] The matching problem: connections to the Gaussian free field via large-scale linearization of the Monge-Ampere equation / Author of the conference Otto, Felix.
- [Multi angle] $L^2$ Hypocoercivity / Author of the conference Dolbeault, Jean.
- [Multi angle] Exponential stability of BV solutions in a model of granular flow / Author of the conference Caravenna, Laura.
Bibliography
- LABBÉ, Cyril, LACOIN, Hubert, et al. Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling. The Annals of Probability, 2019, vol. 47, no 3, p. 1541-1586. - https://hal.archives-ouvertes.fr/hal-01428017
