Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process

Abstract

We find the formulas of the transition probabilities of the $N$-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the final state is the same as the order of particles in the initial state.

References in corpus (10)

• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Spatial correlations of the 1D KPZ surface on a flat substrate
• Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles
• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• On the asymmetric simple exclusion process with multiple species
• Determinant representation for some transition probabilities in the TASEP with second class particles
• The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates
• The current distribution of the multiparticle hopping asymmetric diffusion model
• On the TASEP with Second Class Particles
• Determinantal Expressions in Multi-Species TASEP

Cited by in corpus (4)

• KPZ fluctuations in finite volume
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Integrability of the multi-species TASEP with species-dependent rates
• Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles