The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension
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10955_2015_Article_1218.pdf
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Author(s)
Corwin, Ivan
Petrov, Leonid
Date Issued
February 2015
Journal
Journal of Statistical Physics
Publisher
Springer-Verlag
Citation
Corwin, Ivan, and Leonid Petrov. “The q -PushASEP: A New Integrable Model for Traffic in 1 + 1 Dimension.” Journal of Statistical Physics, vol. 160, no. 4, February 2015, pp. 1005–1026.
Version
Author's final manuscript
Abstract
We introduce a new interacting (stochastic) particle system q-PushASEP which interpolates between the q [italicized q]-TASEP of Borodin and Corwin (Probab Theory Relat Fields 158(1–2):225–400, 2014; see also Borodin et al., Ann Probab 42(6):2314–2382, 2014; Borodin and Corwin, Int Math Res Not 2:499–537, 2015; O’Connell and Pei, Electron J Probab 18(95):1–25, 2013; Borodin et al., Comput Math, 2013) and the q-PushTASEP introduced recently (Borodin and Petrov, Adv Math, 2013). In the q [italicized q]-PushASEP, particles can jump to the left or to the right, and there is a certain partially asymmetric pushing mechanism present. This particle system has a nice interpretation as a model of traffic on a one-lane highway. Using the quantum many body system approach, we explicitly compute the expectations of a large family of observables for this system in terms of nested contour integrals. We also discuss relevant Fredholm determinantal formulas for the distribution of the location of each particle, and connections of the model with a certain two-sided version of Macdonald processes and with the semi-discrete stochastic heat equation.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10955-015-1218-9
