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The speed of a second class particle in the ASEP
Multi angle
Authors : Saenz, Axel (Author of the conference)
CIRM (Publisher )
34E20 - Singular perturbations, turning point theory, WKB methods
60B20 - Random matrices (probabilistic aspects)
34M50 - nverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Presentation(AxelSaenz).pdf
CIRM (Publisher )
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Abstract :
In this talk, we discuss the application of the Yang-Baxter equation for the quantum affine lie algebra $U_{q} \left (\widehat{ {\mathfrak{sl}}_{n+1}} \right )$ to interacting particle systems.
The asymmetric simple exclusion process (ASEP) is a continuous-time Markov process of interacting particles on the integer lattice. We distinguish particles to be either a first class or a second class particle. In particular, the second class particles are blocked in their movement by all other particles, while the first class particles are only blocked by other first class particles. We consider the step initial conditions so that all non-negative integer positions are occupied and all other positions are vacant at time zero. Moreover, we take exactly L second class particles to be located at the very front of the configuration at time zero. Then, using recent results of Tracy-Widom (2017) and Borodin-Wheeler (2018), we compute the asymptotic speed of the leftmost second class particle.
This is joint work with Promit Ghosal (Columbia University) and Ethan Zell (University of Virginia) in arXiv:1903.09615.
MSC Codes : The asymmetric simple exclusion process (ASEP) is a continuous-time Markov process of interacting particles on the integer lattice. We distinguish particles to be either a first class or a second class particle. In particular, the second class particles are blocked in their movement by all other particles, while the first class particles are only blocked by other first class particles. We consider the step initial conditions so that all non-negative integer positions are occupied and all other positions are vacant at time zero. Moreover, we take exactly L second class particles to be located at the very front of the configuration at time zero. Then, using recent results of Tracy-Widom (2017) and Borodin-Wheeler (2018), we compute the asymptotic speed of the leftmost second class particle.
This is joint work with Promit Ghosal (Columbia University) and Ethan Zell (University of Virginia) in arXiv:1903.09615.
34E20 - Singular perturbations, turning point theory, WKB methods
60B20 - Random matrices (probabilistic aspects)
34M50 - nverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Presentation(AxelSaenz).pdf
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 09/05/2019 Conference Date : 11/04/2019 Subseries : Research talks arXiv category : Probability ; Mathematical Physics Mathematical Area(s) : Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:41:20 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-11_Saenz.mp4 
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Information on the Event
Event Title : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial DataEvent Organizers : Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken Dates : 08/04/2019 - 12/04/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2104.html
Citation Data
DOI : 10.24350/CIRM.V.19517503Cite this video as: Saenz, Axel (2019). The speed of a second class particle in the ASEP. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19517503 URI : http://dx.doi.org/10.24350/CIRM.V.19517503 |
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Bibliography
- Ghosal, P., Saenz, A., & Zell, E. C. (2019). Limiting speed of a second class particle in ASEP. arXiv preprint arXiv:1903.09615. - https://arxiv.org/abs/1903.09615
- Tracy, C. A., & Widom, H. (2017). Blocks in the asymmetric simple exclusion process. Journal of Mathematical Physics, 58(12), 123302. - https://arxiv.org/abs/1711.08094
- Borodin, A., & Wheeler, M. (2018). Coloured stochastic vertex models and their spectral theory. arXiv preprint arXiv:1808.01866. - https://arxiv.org/abs/1808.01866
