2013/08/14 by Ivan Corwin, Leonid Petrov, Corwin, Ivan +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1308.3124
22 pages; 4 figures. v2: minor improvements of presentation and discussions. To appear in Journal of Statistical Physics
openalex publication_date 2013/08/14 · arxiv created 2015/03/19 · arxiv updated 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new interacting (stochastic) particle system q-PushASEP which interpolates between the q-TASEP introduced by Borodin and Corwin (see arXiv:1111.4408, and also arXiv:1207.5035; arXiv:1305.2972; arXiv:1212.6716) and the q-PushTASEP introduced recently by Borodin and Petrov (arXiv:1305.5501). In the 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 in which cars are able to accelerate or slow down. 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.