The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension

Abstract

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.

22 pages; 4 figures. v2: minor improvements of presentation and discussions. To appear in Journal of Statistical Physics

References in corpus (3)

• Spectral theory for the q-Boson particle system
• A q-weighted version of the Robinson-Schensted algorithm
• Height fluctuations for the stationary KPZ equation

Cited by in corpus (6)

• Lectures on Integrable probability: Stochastic vertex models and symmetric functions
• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• Markov duality and Bethe ansatz formula for half-line open ASEP
• Law of Large Numbers for Infinite Random Matrices over a Finite Field
• Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP