On the asymmetric simple exclusion process with multiple species

Abstract

In the asymmetric simple exclusion process on the integers each particle waits exponential time, then with probability p it moves one step to the right if the site is unoccupied, otherwise it stays put; and with probability q=1-p it moves one step to the left if the site is unoccupied, otherwise it stays put. In previous work the authors, using the Bethe Ansatz, found for N-particle ASEP a formula --- a sum of multiple integrals --- for the probability that a system is in a particular configuration at time t given an initial configuration. The present work extends this to the case where particles are of different species, with particles of a higher species having priority over those of a lower species. Here the integrands in the multiple integrals are defined by a system of relations whose consistency requires verifying that the Yang-Baxter equations are satisfied.

17 pages. Version 3 corrects misprints, clarifies some points, and adds references

References in corpus (7)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Exact height distributions for the KPZ equation with narrow wedge initial condition
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Spectrum in multi-species asymmetric simple exclusion process on a ring
• Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
• Recursive structures in the multispecies TASEP
• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring

Cited by in corpus (15)

• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
• Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
• Limiting current distribution for a two species asymmetric exclusion process
• Inhomogeneous generalization of multispecies totally asymmetric zero range process
• 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
• Integrable Structure of Multispecies Zero Range Process
• Some conditional probabilities in the TASEP with second class particles
• 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
• Distribution of a second-class particle's position in the two-species ASEP with a special initial configuration