The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension
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...
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| Format: | Article |
| Language: | English |
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Springer-Verlag
2016
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| Online Access: | http://hdl.handle.net/1721.1/104842 |
| _version_ | 1826209083347173376 |
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| author | Corwin, Ivan Petrov, Leonid |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Corwin, Ivan Petrov, Leonid |
| author_sort | Corwin, Ivan |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:17:17Z |
| format | Article |
| id | mit-1721.1/104842 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:17:17Z |
| publishDate | 2016 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/1048422022-09-28T19:47:32Z The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension Corwin, Ivan Petrov, Leonid Massachusetts Institute of Technology. Department of Mathematics Corwin, Ivan 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. National Science Foundation (U.S.) (DMS-1208998) Russian Foundation for Basic Research (Grant 11-01-93105) Microsoft Research (Schramm Memorial Fellowship) Clay Mathematics Institute (Clay Research Fellowship) 2016-10-17T14:33:34Z 2016-10-17T14:33:34Z 2015-02 2014-11 2016-08-18T15:44:37Z Article http://purl.org/eprint/type/JournalArticle 0022-4715 1572-9613 http://hdl.handle.net/1721.1/104842 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. en http://dx.doi.org/10.1007/s10955-015-1218-9 Journal of Statistical Physics 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. Springer Science+Business Media New York application/pdf Springer-Verlag Springer US |
| spellingShingle | Corwin, Ivan Petrov, Leonid The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension |
| title | The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension |
| title_full | The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension |
| title_fullStr | The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension |
| title_full_unstemmed | The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension |
| title_short | The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension |
| title_sort | q pushasep a new integrable model for traffic in 1 1 dimension |
| url | http://hdl.handle.net/1721.1/104842 |
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