Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems

Abstract

This paper presents the exact expressions of the transition probabilities of some non-determinantal Bethe ansatz solvable interacting particle systems: the two-sided PushASEP, the asymmetric avalanche process and the asymmetric zero range process. The time integrated currents of the asymmetric avalanche process and the asymmetric zero range process are immediate from the results of the asymmtric simple exclusion process.

Version 4 corrects errors in the proof of transition probabilites

References in corpus (9)

• Asymptotics in ASEP with Step Initial Condition
• Fluctuation properties of the TASEP with periodic initial configuration
• A Fredholm Determinant Representation in ASEP
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Total Current Fluctuations in ASEP
• On ASEP with Step Bernoulli Initial Condition
• The Asymmetric Avalanche Process
• Dimers and orthogonal polynomials: connections with random matrices

Cited by in corpus (6)

• On integrability of zero-range chipping models with factorized steady state
• Spectral theory for the q-Boson particle system
• The Transition Probability of the $q$-TAZRP ($q$-Bosons) with Inhomogeneous Jump Rates
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• The current distribution of the multiparticle hopping asymmetric diffusion model
• Current statistics in the q-boson zero range process