Determinant representation for some transition probabilities in the TASEP with second class particles

Abstract

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.

Minor revision; journal reference added

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Cited by in corpus (13)

• Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
• Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
• Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• Determinantal Expressions in Multi-Species TASEP
• KPZ fluctuations in finite volume
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• On the TASEP with Second Class Particles
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Some conditional probabilities in the TASEP with second class particles
• Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles
• Integrability of the multi-species TASEP with species-dependent rates
• Distribution of a second-class particle's position in the two-species ASEP with a special initial configuration